Our analysis considers the extent to which airborne coral reef remote sensing may be environmentally limited by spatial variation in water column properties and depth, operating in conjunction with other environmental factors such as sub-pixel mixing from benthic classes of mixed composition, i.e., spatial resolution vs. heterogeneity, sea surface state and sun elevation (Figure 3(b)). A modelling and sensitivity analysis was performed in which the spectral separability of benthic classes was assessed under a set of scenarios each representing a different combination of environmental factors and sensor characteristics. By comparing achievable separability under different scenarios the effects of individual environmental factors were assessed, such as the difference between separability at specific depths as opposed to separability when the benthic classes occur across a range of depths. Previous work has considered sensor spectral band configurations for coral reef applications [6,7]. For statistical validity, given the large number of degrees of freedom in configuring a hyperspectral sensor, this requires a very substantial dataset of reflectances (i.e., 1,000’s). So to simplify the analysis here, we used a single configuration of sensor wavelength bands throughout (Table 1) and concentrate on sensor noise and sub-pixel mixing, the latter being analogous to the effect of spatial resolution. The band choices are based on a review of coral and algal pigment absorption features from spectroscopy and remote sensing [4], and actual configurations of the Compact Airborne Spectrographic Imager (CASI) used in previous studies which have demonstrated discrimination of live and dead coral [2,3]. The structure of the methods and analysis are summarised in the flowchart of Figure 3(a), and the details are presented in the following sections.

The sensitivity analysis involved modelling the distribution of sensor recorded spectral reflectance for each benthic class under specific scenarios defined by the other environmental and sensor factors. Note we use the term “scenario” to represent a particular combination of environmental factors and sensor configuration (Figure 3(b), Table 2). The separability of the reflectance distributions for differing benthic compositions (Figure 1) under a given class combination scenario indicates the extent to which that particular combination of environmental factors and sensor configuration confounded separability for those benthic classes.

In the benthic remote sensing literature the concept of “class” is often restricted to benthos, since “classification” of image pixels to benthic classes is usually the final aim [22]. However, as Mobley [23] discusses, the translation of class structured analyses as used in terrestrial applications to sub-surface aquatic environments is problematic, since benthic composition is only one of several environmental and sensor factors that contribute to the sensor recorded signal. In our analysis we conceive a class structure for the other environmental factors and sensor configurations (Table 2). For example, in the same way that the pure Live Coral benthic class was modelled as a set of reflectance spectra from live corals, the Zonal IOP class was modelled as a set of water optical properties collected across different reef zone locations. This is conceptually similar to the structure of image analysis methods which use look up tables or model inversions based on a range of water optical properties [16,18] but here some classes are explicitly constructed to encompass within-class variance of the parameters in question. By this method, parameters often treated as quantitative, such as depth [16] can be class structured by quantizing the value range in a manner suitable for the application and then grouping discrete values into classes (Table 2).

The class structure of the sensitivity analysis included thirteen benthic classes (based on linear spectral mixes of four basic benthic types, each represented by a number of spectra, Table 3), five water inherent optical property (IOP) classes, six depth classes, two sun position classes, two wind speed classes and three sensor SNR classes (Table 2, Figure 2(b)). A “scenario” therefore refers to modelling of sensor recorded reflectance distribution under a specific combination of the environmental and sensor classes. The overall structure of the results was therefore 6-dimensional, with every possible combination of the different classes evaluated giving 4,680 scenarios (Figure 2(a)). The reflectance distributions for each of these scenarios were then compared to assess the spectral separability of the scenarios based on 100% Live Coral cover from the corresponding scenarios for the other twelve benthic classes (corresponding scenarios have all other environmental and sensor classes the same). This gave a total of 4,320 individual separability evaluations: three groups of 1,440 scenarios corresponding to discrimination of pure Live Coral from mixtures containing Bleached Coral, Dead Coral/Turf and Macroalgae respectively. For each of these three benthic class groups a hierarchical master analysis (described below) organised the 1,440 results into a graph diagram structure revealing the most significant environmental and sensor classes with respect to reducing the separability of the benthic compositions from pure Live Coral.

The benthic classes were each initially represented by a set of in situ recorded spectral reflectances linearly mixed according to the benthic composition (Table 3, Figure 4, collection methods given in [24]). In the analysis these basic reflectance spectra were translated by modelling to give total spectral reflectance above the water surface, R_t, based on the parameters defined by a given set of the other system component classes and incorporating sensor noise. For example, an initial set of 200 in situ reflectance spectra of benthic class for pure Live Coral could, in one scenario, be modelled to give 200 above-surface reflectance spectra under clear water conditions, 5 m depth, wind speed of 2 ms⁻¹ and sun zenith angle of 15°. However, like the benthic classes, some environmental component classes were also based on multiple data to express their within-class variance. For example, the Zonal IOP class (Table 2) consisted of five different IOP datasets from different reef locations; in this case the modelling process would result in 1,000 R_t spectra, the distribution of which embodies both variance in benthic reflectance and water optical properties. By assessing the spectral separability of two benthic classes based on their modelled R_t spectra under a given combination of system components the impact of the additional sources of variance was assessed.

The technical steps in the modelling process were as follows. The benthic class reflectance spectra, IOPs and input sky irradiances (Table 2) were resampled to a typical 15-band CASI sensor configuration (Table 1) prior to the modelling phase. The modelling of R_t from benthic reflectance was performed using PlanarRad, an open-source implementation of the invariant imbedded algorithm for directional “quad-averaged” radiances in plane-parallel waters. This software is functionally equivalent to the commercial software Hydrolight and has been validated against both Hydrolight and other models [31,32] (and unpublished data). Total above-water reflectance was calculated as R_t = L_u/E_d, where L_u is the upwelling radiance and E_d is downwelling irradiance just above the water surface. We use R_t since unlike the usual definition of remote sensing reflectance, R_rs, [27] our use of L_u (and hence R_t) includes reflection from the water surface. This may be an important confounding factor for benthic separability since a high sun-glint signal increases magnitude of SNR-based sensor noise, which being stochastic cannot be corrected for even if the sun-glint component itself can be removed [33]. Sensor noise was incorporated onto the R_t spectra produced by the water column model by translating each R_t into 30 new spectra each of which had random noise terms added in each band based on the sensor SNR class for that scenario (Table 2). The figure of 30 was chosen heuristically prior to the main analysis with the objective being to fully populate the signal noise in the 15-band spectral space without excessive redundancy.

The water column model requires depth-averaged water inherent optical properties as input (Table 2, Figure 5). These data were collected at various reef locations in Palau, Micronesia, in March 2006 using a WET Labs AC-S, measuring the non-pure water fraction beam attenuation and absorption in 85 bands from 400 nm to 740 nm, and a WET Labs ECO-BB3 backscatter meter, measuring backscatter at 117° at 470 nm, 532 nm, and 660 nm. The AC-S data were subject to full temperature, salinity and scattering corrections as described in the WET Labs protocol document and [34]. The resulting non-pure water fraction absorption (typically denoted a) and attenuation (c) were added back onto pure water values [35] to give the total a, b (scattering) and c values for modelling purposes (Figure 5). The backscatter at 117° was processed to estimate total particulate backscatter B_p as described in [36], and this formed the basis for the estimation of three Fournier-Forand phase functions, at 470 nm, 532 nm, and 660 nm, according the methods described in [37] with functions for other wavelengths derived by linear interpolation. With respect to modelled diffuse attenuation for sun zenith 15°, the range in the IOP data set is greater than that of Jerlov types IB to 1 (Figure 5) but slightly less than that of a previously published Caribbean diffuse attenuation dataset [38].

To assess spectral separability between scenarios it was desired to find a measure which approximates to the intuitive notion of class overlap in spectral space (Figure 1). The method used here was to attempt to insert a separating plane in spectral space between the modelled reflectances of the two benthic types (Figure 1). The inverse of the grouped covariance matrix is one way to establish such a plane and is similar to linear discriminant analysis (LDA) [39]. For each pair of benthic classes and a specific set of treatments (a scenario) the set of n R_t spectra representing each class was used to establish a dividing plane in spectral space (Figure 1) and the number of individual spectra lying on their correct class side of the plane was counted as n_c. Note that n_c ranges from n to 2n since there are a total of 2n spectra and a separating plane can always be found such that half the points are on the correct class side (Figure 1). Separability, τ, was then calculated as, (1) τ = 100 × n c − n n ( % )

In practice, the range of τ is 0% (completely inseparable classes) to 100% (completely separable) and has identical interpretation to the Tau coefficient [40] as the percentage more correct classifications achieved than would be expected by chance alone [22]. An individual τ value has no associated statistical significance and is simply a number that approximates to the fundamental separability between the spectral distributions for a specific model evaluation (Figure 1).

The fully factored sensitivity analysis contained 4,680 class combinations (i.e., scenarios) that corresponded to modelling approximately 1,560,000 R_t spectra, before the addition of sensor noise. For each comparison between scenarios the τ value gives the resultant separability for that particular model evaluation with no associated statistical significance. However, since some classes contained stochastic elements, e.g., benthic class mixtures and sensor noise, the predicted separabilities are estimates of what would be expected under many model runs for the given scenarios. To assess the spread of these estimates the entire analysis was repeated ten times. In the results the mean separabilities (τ̄) are reported with reference to their standard error over the ten runs. Where required, t-tests were applied to these mean separabilities to determine if an apparent change in separability were genuine or an artefact of the specific instantiations of stochastic components of the model. Where this was done simultaneously across several scenarios both the standard and Dunn-Ŝidák Type I error corrected results were calculated [41].

With 4,680 class combinations in a 6-dimensional results table further condensing of the results is required to get an overview of relative importance of the different factors. Here we present a general method of constructing a hierarchical class significance diagram from a fully factorised sensitivity analysis (Figure 6).

The diagram consists of a directed graph (meaning “graph” as in graph theory [42]) that is built starting with a single vertex representing the entire results, i.e., all scenarios, and then scenarios including specific classes are iteratively excluded with the classes chosen in order to maximally increase the overall accuracy at each step. The result is a directed graph where each arc represents the exclusion of a class from the entire results table and vertices represent the resulting subsets of scenarios. The vertical position of a vertex in the diagram is based on the mean separability over the set of scenarios that it represents. Therefore the relative effect of excluding successive confounding classes is readily apparent. The horizontal position of vertices has no meaning and is merely based on spacing out the vertices at each level. The graph is built iteratively, for each current vertex each class is removed in turn and the increase in overall accuracy noted. Then new vertices and arcs are added corresponding to the class giving the highest increase in overall accuracy when excluded, and any other classes which have an effect on overall accuracy of at least half as much as the highest. More than one class may be added at each step since, for example, excluding the depth class of 20 m from the results might cause a similar increase in overall accuracy to removing the Zonal IOP class. In addition, different “routes” from low to high accuracy may merge to give collections of classes that jointly act to confound accuracy. Figure 6 illustrates the construction of a hierarchical class significance diagram from a simple hypothetical three-factor sensitivity analysis.

The baseline in situ spectral separability of Bleached Coral, Dead Coral and Macroalgae from Live Coral both as pure class spectra and as mixtures in pure Live Coral was generally high (Figure 7). All three types were highly separable from Live Coral in 100% proportions, for class sizes of n ≥ 200, Dead Coral and Macroalgae had separabilities τ > 90% and Bleached Coral τ > 80%. This result agrees with previously published results that fundamental reef benthic classes are highly separable by their basic in situ reflectance spectra [6]. However, separability between pure Live Coral and Live Coral mixed with small proportions of the other benthic types was significantly lower, dropping to τ< 30% for mixtures of proportion 0.05. Previously published work [7] has shown that classification of linearly mixed in situ spectra of coral, algae and sand generally classifies to the dominant benthic type. Our results do not contradict this, but additionally indicate that non-dominant proportions do retain some statistical separability, at least to sub-pixel proportions of 0.2. However, in practical terms separabilities less than 50% accuracy should be considered quite weak.

The estimated separability of pure Bleached Coral from pure Live Coral was the lowest of the three pure classes, τ = 81% separable vs. 92% and 93%, n = 200. However, Bleached Coral separability was more robust in small proportions than for the other benthic types, with a 0.2 proportion of Bleached Coral giving τ = 57% separability vs. 48% for Dead Coral and 32% for Macroalgae (Figure 7). This pattern may have two explanations: (i) an artefact due to the relatively low number of bleached spectra in the spectral library, or (ii) due to a bimodal or otherwise non-uniform relative spectral distribution of the Live Coral and Bleached Coral types, if there were two “types” of Bleached Coral, for example. The bleached coral spectral library has a far greater diversity of spectral shapes than the other benthic types (Figure 4). There is a wide range of overall reflectance, some spectra contain host pigment fluorescence features [4] in the region 450–650 nm and chlorophyll features often persist from remaining symbionts or endolithic algae [4]. Almost all the bleached spectra were collected at a single site (Keppel Islands, Australia) but the spectral diversity is higher than previously published partially bleached coral spectra [43]. However the impact of this diversity on overall separability is nevertheless small since τ = 81% still predicts pure Bleached Coral and Live Coral to be highly separable.

Estimated benthic class separabilities across the sensitivity analysis are the result of the interaction of all the modelled factors of benthic composition, sun elevation, wind speed, absolute depth, depth variation, absolute water clarity and variation in water clarity (Figures 8 and 9). Although strictly speaking each factor cannot be treated in isolation, some generalisations can be made. Basic trends and interesting observations are summarised in Table 4 and will be discussed briefly in this section.

In general, separability was significantly enhanced at the lower sun position zenith angle of 45° vs. 15° but variation in depth or low cover proportions are more severely limiting and reduced the beneficial effect (Table 4, Figures 8 and 9). Nevertheless t-tests indicated that the majority of Live Coral vs. Dead Coral or Macroalgae scenarios have significantly improved separability with low sun elevation (Table 4).

The physical basis of the advantage of low sun elevation is in reduced reflection from the air-water interface into upward radiance, L_u. For high sun elevations the benthic component is a smaller fraction of the overall larger upwelling radiance and so is increasingly obscured by sensor signal-dependent noise (SNR). This is supported by the results, however while for specific depths SNR was more limiting at high sun elevation, the effect of sun elevation itself is a greater (Figure 8). Further, when the distribution of modelled spectral reflectances (R_t) included within-image depth variation (Figure 9) the difference in separability due to sun elevation seen at specific depths (Figure 8) was almost completely absent although some SNR limitation at 400:1 and 200:1 (not shown) is still evident. These results are consistent with those presented in [9] for a simple scenario based on a HyMap image and Case 1 waters. In that study the combined sensor and environmental noise, SNR_E, in a HyMap image differed from 100:1 to 20:1 in the presence of sun glint, and consequently the calculation of theoretical depth at which live coral vs. dead coral can be discriminated in the clearest Case 1 reef waters is 25 m vs. 8 m, respectively. This result is comparable to a single class combination in our analysis, for the Clear IOP class, separability of Live Coral and Dead Coral at specific depth 5 m under high sun position (86%) is the same as at specific depth 20 m for low sun position (87%) but substantially lower with high sun position at 20 m (56%) (Figure 8, wind speed 2 ms⁻¹, SNR 800:1). However the cited study [9] did not consider the contribution to environmental noise (SNR_E) of spatial variance in IOPs or depth and also did not assess the possibility of across-depth confusion between benthic classes. These factors are incorporated into our analysis by the other treatment combinations (Table 4), and show that this specific-depth clear water result is a best case scenario for live and dead coral discrimination.

In a practical remote sensing application, the spectral distribution of above-water reflectances for a given benthic class will be subject to variance caused by differences in depth. If the depth at given pixel is unknown, the spectral reflectance could represent any benthic class at any depth within the image depth range (Figure 2). In the sensitivity analysis this corresponds to the situation where the sets of R_t representing benthic classes are modelled under a scenario involving one of the multiple-depth classes Shallow, Shallow-Mid or Shallow-Deep (Table 2). Spectral variation caused by depth variation is in itself likely to decrease the separability of the benthic classes (Figure 1). In contrast, the limiting role of absolute depth, assessed as benthic class separability at a specific uniform depth, occurs only in conjunction with other sources of variance. For example in deep water, differences in spectral reflectance may be lower than sensor SNR thresholds, so the variance due to SNR is the fundamental cause of the inseparability. The effect of depth on separability therefore operates by two distinct mechanisms and variance in depth may in itself be limiting by increasing across-depth confusion between classes irrespective of sensor SNR (Figure 1). This reasoning is supported by the results, where the effect of variance in depth in general overwhelms the effects due to IOP class, sun elevation or sensor SNR (Table 4, Figure 9). In particular, the strong effect of sensor SNR seen at specific absolute depths below 5 m (Figure 8) is largely absent under depth variation (Figure 9), so attainable accuracy is no longer “sensor limited” but is “environmentally limited” (upper right hand part of Figure 1).

Although variation in depth reduced the significance of other factors such as sensor SNR on benthic class separability, determining the overall effect of depth variance itself, as an isolated concept, on achievable accuracy is less straightforward. From Figures 8 and 9 it appears as though overall separability under the multiple-depth classes might simply be the average separability under the specific depths within those classes. For example, if τ̄_S–DEEP is separability under the Shallow-Deep multiple-depth class and τ̄_d is separability at specific depth d m, then maybe τ̄_S–DEEP ≈ (τ̄_0.5 + τ̄₂ + τ̄₅ + τ̄₁₀ + τ̄₂₀)/ 5, since the Shallow-Deep class is constructed from the five specific depths 0.5, 2, 5, 10 and 20 m (Table 2). If the above relation were true then there would be no evidence for across-depth confusion between benthic classes and the effect of variation in depth could simply be interpreted in terms of the separabilities at the specific absolute depths involved. In fact, with respect to discriminating Live Coral from any of the other classes in pure 1.0 proportion, in 294 of 360 cases across the entire analysis the separability estimate under a multiple-depth class was significantly worse than the mean separability of the corresponding individual depths (p < 0.01, Dunn-Ŝidák correction applied). Separability results for many of the benthic classes with mixture proportions less than 1.0 were similarly conclusive, with the pattern only breaking down for low mixture proportions of 0.2 and 0.05, which have very low separabilities anyway.

One caveat to be considered is that the decrease in separability observed under depth variation may be an artefact of the linear separating plane (Figure 1) if depth variation produced a curved pattern of reflectance distribution in spectral space. In this case less constrained analysis methods such as successive approximation or lookup tables [17,18,20] or by applying a linearising pre-classification transform [44]. However, although the non-linear distribution argument will have some validity in general, it is an unlikely explanation of the observed results in this case for two reasons: (i) the Shallow multiple-depth class only contains two depths so depth variation alone cannot cause a non-linear distribution of R_t; and (ii) variation in IOPs would be expected to produce a similar non-linear effect in spectral distributions, but in fact in this study variation in IOPs had relatively less effect on separability than variation in depth (Figures 8 and 9).

In a practical application, sources of environmental noise other than depth variation will be present and may also be limiting, for example atmospheric effects, which we neglect here. Our results indicate that it may be necessary to re-evaluate conclusions from previous studies that only consider differences between benthic types at specific uniform water depths without possibility of across-depth confusion [9].

Finally, by way of a comparison to field-based data, we consider a published Pacific study [3] that demonstrated an improved ability to discriminate live from dead coral in approximate depth ranges of 2–3 m vs. 3–4 m in a 0.25 m pixel CASI image (SNR ∼400:1) collected with solar zenith angle ∼50°. In contrast, the modelling results here indicate no difference in separability for these classes in clear or lagoonal waters at specific depths of 0.5 m and 5 m for sun zenith 45° but a clear significant difference for sun zenith 15° or waters of lower clarity (Figure 8, centre left). However, the imagery in the published study [3] had only 6 spectral bands so our relative over-prediction of separability in the deeper waters may be due to the higher 15-band spectral resolution in the model. Extending the model framework to incorporate different spectral sensor configurations will answer this question and is a priority for future work.

Analogous to the previous discussion on depth, a distinction can be drawn between the effects of absolute water clarity on benthic class separability as opposed to the effects of variance in optical properties within an image. While neither absolute water clarity nor variance in clarity had much effect on benthic class separabilities in very shallow waters (0.5 m) absolute clarity within the modelled range starts to become limiting beyond 5 m while Zonal and Fluvial levels of variance have some effect at depths below 0.5 m (Table 4, Figure 8). Therefore, absolute water clarity and Tidal or Zonal IOP variation in the absence of terrestrial inputs and at moderate depths (<5 m) seems not to be a major confounding factor for benthic class separability. Since these conditions correspond to those found for much of coral reef remote sensing objectives then suitable analysis algorithms should be able to factor out water column effects [16,18,20,45]. Interpreting the total water column optical effect in terms of optical depth (optical depth = depth × attenuation), then it is clear that variation in depth will be more significant optically than the IOP variation in our dataset. Ratios between optical depths among the three physical depths 0.5, 5 and 20 m are 4, 10 and 40. Whereas relative attenuation between the IOP datasets has a maximum ratio of only around 10, or around 5 if the Fluvial class IOP datasets are excluded (Figure 5). If the ratio of 5, between minimum and maximum attenuations in the Lagoon class, is assumed as the typical range for reef remote sensing, then variation in IOPs will only become more optically significant than variation in depth if the depth range is restricted such that d_max/d_min < 5, for example, a depth range of 1 to 5 m or 2 to 10 m.

Discrimination of pure Bleached Coral from pure Live Coral presents an exception to the previous observation that Tidal variation IOPs overall had little effect (Figure 8, top left). While no significant difference exists in Bleached Coral separability under the single-dataset Clear or Lagoon classes, τ̄ = 81% in both cases, Tidal IOP variation significantly reduces separability of Bleached Coral from Live Coral to τ̄ = 74% (p< 0.001). This pattern occurs at both wind speeds (2 ms⁻¹ and 8 ms⁻¹) but only for the high 800:1 SNR class and not when discriminating mixed proportions of Bleached Coral in Live Coral less than 1.0 (Figure 8, top right). In most cases sediments in coral reef environments will be dominated by calcium carbonate particles, and this was certainly true in our study sites where coral sand was abundant. Since detection of coral bleaching by remote sensing is essentially detecting a calcium carbonate “signal”, i.e., the coral skeleton with pigments removed, it is possible that variation in suspended sediments may be a confounding factor specifically for the detection of bleaching. Our results support this hypothesis; in particular Figure 10 also indicates that variation in depth in Lagoon waters is a particular confounding factor for detecting Bleached Coral and also for Dead Coral, but less so Macroalgae. With respect to total water column backscatter, variation in depth under constant sediment load will to some extent act analogously to variation in sediment load. Therefore, both tidal depth in the presence of suspended sediments and changes in suspended sediment load may complicate detection of bleaching by optical remote sensing.

The vast majority of benthic class discrimination scenarios considered in the sensitivity analysis were not sensor-noise limited in the range of sensor SNR of 200:1 to 800:1. Of all 1440 class combination scenarios produced for both SNR 200:1 and SNR 400:1 only in 194 cases was there an increase in benthic class separability of five percentage points or more for the SNR 400:1 result, i.e., 13% of the results were sensor-noise limited at the SNR 200:1 vs. 400:1 level. A threshold change in τ̄, Δτ̄ ≥ 5% was chosen to define a practical “limited” scenario rather than evaluating statistical significance of differences in τ̄, since τ̄ values can be statistically different by very small irrelevant amounts. By this criteria, the benefit of SNR 800:1 vs. 400:1 was even less significant, with 88 of 1,440 scenarios giving an SNR choice separability increase τ̄ > 5%., i.e., only 6% of scenarios were sensor-noise limited.

Fundamental benthic class in situ spectral variation could be considered part of the “environment” and is always to some extent limiting since 100% separabilities were not achieved even with in situ reflectances (Figure 7). However, since here we are primarily concerned with the water column effects we consider “environmentally limited” scenarios to be those that were not limited by sensor SNR but for which separability was nevertheless reduced below the in situ maxima with Δτ̄ ≥ 5% . By this criteria, 90% of scenarios were subject to separability limitation and removing the sensor-noise limited scenarios from this set leaves around 80% of scenarios as environmentally limited by factors other than basic in situ class overlap.

The distribution of scenarios that were sensor-noise limited in the sensitivity analysis was highly dependent on the environmental class combinations. For some specific environmental scenarios SNR limitation is significant (Table 4). In particular, for distinguishing Dead Coral or Macroalgae from Live Coral under sun elevation 45° and wind speed 2 ms⁻¹, doubling of SNR from 200:1 to 400:1 improved separability by greater than 5% for most depth and IOP classes. This implies that only under ideal environmental conditions of low sea surface reflection into upwelling radiance can sensor SNRs greater than 200:1 offer a significant advantage. Interestingly, under these circumstances, at the 200:1 vs. 400:1 SNR choice, almost all the multiple-depth classes were SNR limited whereas at the 400:1 to 800:1 choice none were (Table 4). This indicates the point at which depth variation overwhelmed sensor SNR as a confounding factor was around the SNR 400:1 level. Therefore, within the scope of this study, variation in depth was slightly less problematic for benthic class discrimination than the combination of sea surface state and sun elevation. Conversely, as discussed before, considering absolute depth as modelled by the single-depth classes, sensor-noise limitation continues to be predicted at the SNR 400:1 to 800:1 level under low sea surface reflection (Table 4). This again reiterates the point that considering separability only at specific uniform depths will over-emphasise the importance of sensor SNR.

Finally, note that discrimination of any mixture proportion of Bleached Coral from Live Coral was not sensor limited under almost any class combination scenario (Table 4). This is consistent with the earlier argument developed from the in situ results, that a large part of the Live Coral and Bleached Coral classes are highly separable, and hence do not require high sensor SNR to be discriminated. Unlike the Dead Coral and Macroalgae classes, the separability of Bleached Coral from Live Coral remains quite high as absolute depth increases and is relatively insensitive to sensor SNR (Figure 10). Therefore, different objectives within the scope coral reef remote sensing may demand different optimal sensor designs.

Hierarchical summary diagrams (Figure 6) were constructed from the 1,440 factor combination scenarios to illustrate the relative significance of the various environmental and sensor class choices with respect to the entire sensitivity analysis for each basic benthic type (Figures 11–13). Each diagram should be read from top to bottom starting at the “All Scenarios” vertex, the vertical position of which indicates the mean separability over all 1,440 scenarios. Subsequent nodes indicate the mean separability as scenarios containing the most significant confounding factors are iteratively removed from the analysis (labelled arcs). At the bottom region of the graphs only the “ideal” scenarios for benthic class discrimination remain and the mean separability as represented by vertical position of the individual vertices is close to the maximum attainable under any scenario. The following sections discuss and interpret the patterns in these diagrams (Figures 11–13).