Coral Reefs

, Volume 23, Issue 1, pp 96–108

Learning to predict large-scale coral bleaching from past events: A Bayesian approach using remotely sensed data, in-situ data, and environmental proxies

Authors

    • Australian Institute of Marine Science
    • Cooperative Research Centre for the Great Barrier Reef World Heritage Area
  • Terry Done
    • Australian Institute of Marine Science
    • Cooperative Research Centre for the Great Barrier Reef World Heritage Area
Report

DOI: 10.1007/s00338-003-0361-y

Cite this article as:
Wooldridge, S. & Done, T. Coral Reefs (2004) 23: 96. doi:10.1007/s00338-003-0361-y

Abstract

Ocean warming and coral bleaching are patchy phenomena over a wide range of scales. This paper is part of a larger study that aims to understand the relationship between heat stress and ecological impact caused by the 2002-bleaching event in the Great Barrier Reef (GBR). We used a Bayesian belief network (BBN) as a framework to refine our prior beliefs and investigate dependencies among a series of proxies that attempt to characterize potential drivers and responses: the remotely sensed environmental stress (sea surface temperature — SST); the geographic setting; and topographic and ecological attributes of reef sites for which we had field data on bleaching impact. Sensitivity analyses helped us to refine and update our beliefs in a manner that improved our capacity to hindcast areas of high and low bleaching impact. Our best predictive capacity came by combining proxies for a site’s heat stress in 2002 (remotely sensed), acclimatization temperatures (remote sensed), the ease with which it could be cooled by tidal mixing (modeled), and type of coral community present at a sample of survey sites (field data). The potential for the outlined methodology to deliver a transparent decision support tool to aid in the process of identifying a series of locations whose inclusion in a network of protected areas would help to spread the risk of bleaching is discussed.

Keywords

Coral bleachingBayesian belief networksRemotely-sensed SSTGreat Barrier Reef

Introduction

Coral reef researchers seek to find order and predictability in a system in which the sense of disorder and unpredictability can at times be overwhelming. In ecological studies of reefs, we aspire to understand past and future processes and events sufficiently well that we can make sensible predictions about the state of unseen reefs, now and in the future. These are also questions of importance to reef policy makers and managers, tasked with ensuring reefs retain their qualities, amenity, and productivity for future generations (Reaser et al. 2001; Best et al. 2002; Chadwick and Green 2002). How can researchers communicate the lessons they learn in a manner that is on the one hand, useful for decision makers in management and policy arenas, and on the other, true to the science and its inherent uncertainties?

We are faced with these challenges in relation to coral bleaching on the Great Barrier Reef (GBR). What have we learned from the 1998 and 2002 “bleaching events”, and how might our process of learning, guide actions that may be put in place to minimize future impacts? The basis for this work is a study undertaken by the Australian Institute of Marine Science (AIMS) and CRC Reef Research Centre for The Nature Conservancy (Done et al. 2003; Berkelmans et al. this issue). Our purpose here is primarily to describe the process we undertook to improve our capacity to recognize more- and less-”bleach-prone” reefs, by learning relationships among remotely sensed data, oceanographic models, and ecological survey data within a Bayesian framework. The main scientific findings will be published elsewhere.

Remotely sensed data from a variety of platforms have become important elements in studying the benthic communities and habitats of coral reefs, along with the physical and environmental pressures that impact upon them (e.g. Strong et al. 2000; Andrefouet et al 2002a; Andrefouet et al 2002b). For this study, we had access to routinely collected remotely sensed, daily SST data (Skirving et al. 2002) from which Berkelmans et al. (this issue) derived a proxy measure of heat stress that was a good predictor of presence or absence of bleaching. The map of this index is part of a developed spatial topology for the GBR that also includes maps of reef shape, orientation, and bathymetry (Lewis 2001); which are stored and managed within the AIMS Geographic Information System (Kininmonth et al. 2003). This spatial topology allowed us to characterize the reefs in our central-southern GBR study area not just in terms of their physical proximity to each other, but also in terms of their similarities in reef characteristics and conditions encountered. This provides us with the potential to extrapolate putative impacts and responses from the surveyed reefs to other ‘equivalent’ reefs that were not surveyed due to constraints of time, cost, and logistics.

Our ultimate goal is to be able to make inferences about reef-scale responses to bleaching at the scale of individual coral reefs (typically a few kilometers in length). As such the choice of an appropriate level of spatial aggregation was important. We wanted to utilize the benefits of both low- and high-resolution spatial data. Low-resolution data has the distinct advantage of “averaging out” small-scale, random heterogeneity (i.e. second-order effects) while still capturing the important organized component (i.e. first-order effects), and thereby facilitating inferences about a regional ecological response that are consistent with ecological heterogeneity at the reef scale. High-resolution spatial data, however, is needed to sensibly reflect heterogeneity at the subreefal scale (habitats, zones, depths). In this study, we worked with remotely sensed environmental proxies at resolutions of 50 and 1 km, and with point data for ecological surveys (“sites” a few 10 s of meters across). For the sites, Done et al. (2003) had developed proxies that characterized three main attributes: the level of bleaching at the time of the survey (June-July 2002 — 3–5 months after peak bleaching); the level of coral mortality attributed to coral bleaching; the type of coral community present (in case different species assemblages had different susceptibilities).

The problem was to explain patchiness in coral mortality caused by heat stress in summer (December 2001 to March 2002). The Bayesian approach seemed ideal, given both our eclectic mixture of data types and our wish to have a procedure that allowed us to incorporate and update prior information and beliefs as the analysis progressed. With the Bayesian approach, when one has a high degree of belief in a specific hypothesis based on past experience (i.e. prior belief), and then observes data that are consistent with that hypothesis, the posterior confidence in the hypothesis is strengthened. Being a normative and rational method for decision-making, it emulates the way in which an expert might make decisions within an uncertain information environment. The use of Bayesian belief networks (BBN) facilitates this process (Pearl 1988; Cowell et al. 1999; Wooldridge 2003). A BBN is a form of influence diagram which, when applied in an ecological setting, depicts and quantifies the strength of causal dependency relations among environmental and ecological factors that might influence outcomes of interest – in this case, coral mortality.

In this paper, our goal is to demonstrate how a Bayesian approach helped identify combinations of factors that most effectively predicted differential bleaching impacts in a sample of reefs on the GBR during 2002. We made use of a series of in-situ field surveys undertaken several months after the 2002 bleaching event, in conjunction with a number of descriptive spatial data sets, including archived remotely sensed SST measures (Done et. al 2003). An important motivation for this paper is to draw attention to the potential benefits offered by Bayesian belief networks to provide structure and transparency in the process of identifying a series of locations whose inclusion in a network of protected areas would help spread the risk of bleaching.

Case study: identifying coral reefs with a low risk-of-death

Background

During the southern-hemisphere summers of 1998 and 2002, large regions of the GBR were exposed to heating anomalies, coral bleaching, and related mortality (Berkelmans and Oliver 1999; Berkelmans et al. 2004 this issue). In other parts of the world, Salm et al. (2001) had noted the existence of areas with relatively high coral survival within generally badly affected regions. They suggested that the higher survival tended to be associated with areas of upwelling, strong currents, emergence of corals, strong shading, and/or turbidity. With climate records and models suggesting increasing frequency of anomalous heating events (Hoegh-Guldberg 1999; Lough 2001), scientists are presented with the challenges of (i) identifying places that are most (and least) at risk of bleaching, and (ii) if there are places that are reliably at lesser risk, facilitating the incorporation of this knowledge into the decision maker’s domain. It may, for example, influence decisions regarding their inclusion in, or exclusion from, protected area networks. Low risk areas are likely to be made up of (i) places that by virtue of their physical setting (e.g. geography and oceanography), are unlikely to be exposed to an anomaly capable of causing a bleaching and mortality response, or (ii) places that can resist an anomaly, on account of being in some sense “well adapted” (Fig. 1; Done 2001). Both low risk classes have the potential to be important reservoirs of abundance and biodiversity in coming decades.
Fig. 1

Types of local areas (i.e. B. and C.) that are most likely to have relatively higher coral survival rates as regional sea temperatures rise (Source: Done 2001)

The 2002 Great Barrier Reef (GBR) Bleaching Data Sets

We compiled a number of data sets, all of which were spatially rectified and maintained within the AIMS GIS (Kininmonth et al. 2003), which utilizes the ESRI (http://www.esri.com/) suite of software products.

Ecological characterization and bleaching impact assessments

Following the 2002 Austral summer bleaching event, Done et al. (2003) undertook two cruises to assess patterns of bleaching impact within the Great Barrier Reef Marine Park. The cruises (25 days between June 25 and August 1) documented the local geomorphologic settings, bleaching impacts, and coral mortality at 150 sites at 50 locations on 32 reefs. The locations of the reefs ranged from the southern to the central GBR (a distance of around 1000 km), and from less than 1 km from the coast to the outer edge of the GBR (~100 km from shore – Fig. 2). Sites were chosen to represent a range of reef waters and habitats that had been relatively hotter and cooler in summer 2001–2. This selection was guided before and during the cruises by frequent reference to the spatial patterns of cumulative summer temperature stress stored within the GIS (see next section for details).
Fig. 2

Location of survey sites within the GBR study area. The figure indicates the general location of inner-, mid-, and outer-shelf reefs, and the GBR Lagoon. Note that most of the reefs are surrounded by waters ranging in depth between 15 and 150 m

Along with the coral bleaching impact assessment (see Table 1 for details), each site was assigned a habitat class (Table 2a) and a taxonomic inventory compiled of observed hard and soft corals. The taxonomic data were used to identify four broad community types (Table 2b) that were characteristic of offshore reef slopes (Type 1 and Type 2), offshore reef flats (Type 3), and nearshore fringing reefs (Type 4). The “community type” groupings of the present study were shown to have equivalence with coral communities defined by Done (1982) for the central GBR (Table 1b).
Table 1

Summary of field methods and indices developed to quantify coral bleaching and coral mortality

(i) Each assessment comprised a 20–30 min survey, during which a taxonomic inventory was complied of observed hard and soft corals.

(ii) Four bleaching categories were subjectively rated on a 5-point scale according to its contribution to overall hard coral cover. Notional equivalents are: 1 =1-2 colonies only; 2=5-10%; 3 = 11 —30%; 4= 31—75%; 5 = >75%.

(iii) An independent subjective estimate was made of percentage cover of coral killed in die summer of 2001-2, and attributable to die coral bleaching episode.

(iv) For each site, we calculated two indices of “bleaching impact” (where ∑ signifies the sum of scores for all species censused at a site).

⋅ Bleaching index = (1*∑shadow+2*∑blotchy+3*∑white+4*∑partial dead)/4*(∑OK+ ∑shadow+∑blotchy+∑white+∑partial dead)

⋅ Coral monality = % dead coral / (% dead coral + % live hard coral).

Table 2

Brief description of habitats and coral community types. Also shown is the equivalence of “community-type” groupings of the present study, with coral communities defined by Done (1982) for the central Great Barrier Reef (which is the northern part of the present study area)

(a) Habitats

Mid-shelf and outer-shelf reefs

Outer slope

Reef flats and slopes exposed to the prevailing seas from SE and SW quadrants

Lagoon

Reef flats and slopes and patches on and adjacent to sandy areas enclosed within the arc of the outer slope

Back-reef

Reef flats and slopes on the outer edge of reefs with a broadly NE and NW aspect

Channel

Reef flats and slopes forming die edges of between-reef channels that are tens of metres across

Inner-shelf reefs

Fringing reefs

Reef flats and slopes, regardless of compass aspect

(b) Coral Communities

“Types” of coral communities-this study

Main habitats

Coral communities —Done 1982

‘Classes” of Coral Communities—Done 1982

Type 1

Reef slopes — all habitats of offshore reefs

6. Acropora palifera/Porites,

II-’semi-exposed to sheltered’

7. Porites/Diploastrea

8. Porites “massive/branching”

Type 2

Reef slopes - all habitats of offshore reefs

9 Ispopora/Seriatopora

II- ‘semi-exposed to sheltered”

10. Acropora ‘staghorn”

11. Acropora ‘tabulate/branching”

12. Acropora “tabulate”

Type 3

Reef flat margins — all habitats of offshore reefs

1. Acropora palifera/humilis —

I-’wave-exposed’

A. palmerae variant

2. Acropora palifera/humilis —

A. hyacinthus variant

3.Acropora palifera/humilis —

A. digitifera variant

Type 4

All habitats - inshore fringing reefs

13. Acropora splendida/divaricata

III - “sheltered”

14. Montipora/Pachyseris

15. Galaxea

16. Montipora

17. Goniopora

Heat stress characterization of the thermal environment

A number of spatial indicators were used to characterize the observed patchiness in ocean temperatures and bleaching response. In the following descriptions, reference to remotely sensed SST measurements refers to processed Advanced Very High Resolution Radiometer (AVHRR) SST measurements; as obtained from National Oceanic and Atmospheric Administration (NOAA) satellite platforms. The term “processed” is used to summarize the (i) retrieval, (ii) correction, (iii) SST generation, and (iv) archival system that is implemented by the AIMS AVHRR Archive Processing System (Skirving et al. 2002). The processing procedure results in estimates of the bulk SST (over a depth of ~1 m) for a spatial resolution of 1 km.

Prior thermal environment

In an attempt to characterize the typical broad-scale summer SST pattern, we undertook a standardized principal component analysis (Eastman and Fulk 1993) using composite maximum summertime SST images that were derived from archived monthly SST averages (Skirving et al. 2002) for the period 1990–2000 (n.b. the abnormally hot year of 1998 was excluded from the analysis). Figure 3 displays the first principal component (the proxy “PCA”), and can be interpreted as the characteristic summertime maximum SST pattern over the GBR for the period 1990–2000.
Fig. 3

Spatial variation of the PCA indicator that characterizes the “typical” broad-scale summer SST pattern based on the archived SST records for the period 1990–2000

We chose to utilize the first principal component (most explained variance) instead of simply calculating a long-run mean value for each pixel in an effort to limit the impact of erroneous pixel values resulting from data limitations (e.g. due to cloud cover), calibration issues (e.g. due to a change in the NOAA sensor), and slight image shifting. Whereas a long-run mean can be seriously biased by an erroneous pixel value, the principal component analysis allowed for the comparison of spatial patterns (in a relative sense) across all years, thereby aiding to filter out potential “noise” in the data.

Patterns of cooling

Waters below the thermocline are important sources of cooling for shallow water corals if they can be mixed into surface waters. We used hydrodynamic model predictions (Bode et al. 1997) to derive an ocean current weighted distance surface “cost100 as a proxy indicator for the ease of transport of cool oceanic waters to all parts of the study area. Cost100 assigns zero “cost” to any point at or beyond the 100-m isobath; it costs little for a reef with a strong current flow that leads to and from the 100-m isobath, and it costs a lot for a reef that is at a great distance and has no current connection. Intermediate results occur for combinations of distance and current connection. The idea postulated is that the greater the cost, the lower the cooling potential from this source.

The current data used to develop cost100 was based on model simulations for a maximum flood current during the middle of a spring-neap cycle. We normalized the range of currents within the study region between 0 and 1, and then used these values as “flow resistance weights” (i.e. the larger the current, the lower the flow resistance, and the lower the effective distance). Since the dominant water movement from the prevailing seas is from the southeast, the effective distance from the 100-m isobath was calculated for a northwesterly direction of travel.

For most of the length of the study area, the effective distance from the 100m isobath along the edge of the GBR is strongly correlated to the actual distance (Fig. 4). Therefore in general, the nearer the coast, the higher the “cost” (or in other words, the lower the likelihood) of having cool deep Coral Sea waters mix with the shallow reef waters to ameliorate heat stress. Likewise, the nearer to the Coral Sea, the higher the likelihood of experiencing cool oceanic waters. However, the many exceptions caused by local differences in bathymetry and currents suggest the proxy may capture the “ease of cooling” better than simple distance from the 100-m isobath.
Fig. 4

Spatial variation of the cost100 indicator, representing the “effective” distance from deep, potentially cool water found below the 100-m isobath

Maximum heat stress (1-km resolution)

Based on the analysis of aerial surveys from over 1,200 reefs, Berkelmans et al. (this issue) showed that the best predictor of presence or absence of bleaching was the highest 3-day summer SST (1-km pixels). They found that it correctly predicted the bleaching status (presence-absence) for 73.2% of the reefs surveyed. We thus used this index – termed “max3day,” as our proxy for maximum heat stress (Fig. 5). The map indicates that very hot water (reds, oranges) bathed many reefs in the survey region, right across the reef tract from the coast to Coral Sea. On the other hand, it also indicates how much of the outer reef tract escaped exposure to even brief periods of hot water (blues).
Fig. 5

Spatial variation of the fine-scale heat stress indicator. The fine-scale heat stress indicator was based on the highest accumulated total (at a given 1 km pixel) for any three-day run of daily summer (2002) SST

Maximum heat stress (50-km resolution)

High-resolution (1-km), remotely sensed SST measurements, such as used to create Fig. 5 are not broadly available for most areas of coral reef interest in the world. In contrast, a range of remotely sensed products with a 50-km resolution is widely available from the NOAA online database (http://orbit35i.nesdis.noaa.gov/orad/). We tested the utility of coarser resolution SST data (when used in combination with other finer-scale physical information) to characterize the thermal environment at the scale of individual reefs (i.e. down to 1-km resolution). First, we developed a degraded version of the our 1-km maximum heat stress indicator “max3day” by spatially averaging the 1-km2 pixels (in blocks of 2,500) down to a 50 x 50 km pixel resolution. The retention of the broad-scale pattern and the loss of detailed texture are illustrated in Fig. 6. In an effort to recapture that hidden texture, we endeavored to learn the empirical relationship between the finer-scale max3day (1 km) and the coarse-scale max3day (50 km), given that we also had available to us the fine-scale physical information provided by our PCA and cost100 proxies. As a robust test, we learned the empirical relationship based on the 1998-bleaching event for all 1,994 gazetted reefs of the Great Barrier Reef World Heritage Area. We then tested how well the learned relationship predicted the finer-scale max3day (1 km) for the 2002 event.
Fig. 6

Spatial variation of the large-scale heat stress indicator. The large-scale heat stress indicator was created by averaging the fine-scale (1-km) heat stress indicator (Fig. 5) to a pixel resolution of 50 km.

An exploratory Bayesian analysis

We thus had a series of spatial indicators to describe the potential thermal environment of our study sites, along with the field assessments of coral bleaching, coral mortality, and coral assemblages. We used a Bayesian approach to explore the extent to which the information content of these proxies allows us to predict the vulnerability to bleaching and coral mortality at the 150 study sites, in particular, the ability to infer areas with the greatest likelihood of low coral mortality. For ease of discussion, Table 3 summarizes the proxy indicator variables used in the Bayesian analysis.
Table 3

Summary description of the proxy indicator variables used in the dependency analysis

Proxy Indicator Variable

Description

Cost100

Cost-weighted distance from the 100 m isobath

Habitat

Classified habitat class

Community

Classified coral community types

Max3day

Maximum three-day run of summer SST (2002)

Bleach

Classified bleaching impact

Dead

Classified coral mortality

We used the dependency analysis algorithm of Cheng et al. (2002) to search for structural dependency relations among the information contained within our proxy indicators. First, we imposed the following “expert” knowledge (i.e. our prior beliefs about bleaching resistance, and refined in this study):
·

cost100 and habitat are externally determined drivers (i.e. parent nodes) that cannot be affected by anything else in the coral reef system.

·

community has a direct dependency on habitat.

·

bleach and dead are hypothesis (i.e. event) variables, which can potentially accept dependency linkages from all system variables.

·

In some trials, we also added PCA as an external driver and proxy for the “normal” temperature regime in which each of the 150 study sites was located.

Next, we used the Netica (http://www.norsys.com) network editor to construct a Bayesian belief network (BBN) from the identified structural dependencies. The BBN visualizes the dependency relationships as arcs between our proxy indicator variables, which are represented in the BBN as nodes. The arcs connecting the nodes are directional and point from parent nodes to child nodes, i.e. the intuitive meaning of a directed link is that the parent node has a direct influence on the child node. The absence of a link between two variables indicates conditional independence between them. The strength (i.e. certainty) of the dependency link between a child and its parent node(s) is summarized through a conditional probability table (CPT). The CPT specifies the conditional probability of the child node being in a particular state, given the states of all its parents: P (childparent1, parent2,....parentN). Should a node have no parents, the table reduces to an unconditional one, P (child).

For the present investigation, rather than providing a description of the CPTs, we instead undertook a sensitivity analysis to identify the network components which have the greatest influence on coral mortality. The sensitivity analysis was conducted by systematically varying the values of individual network components to determine how they affected the dead nodal variable.

The power of the BBN as a decision support tool comes to light whenever we change the likelihood of parent states, based on our field evidence (i.e. 150 sites). The effects of the evidence are propagated throughout the dependence-structured network via a probabilistic inference algorithm (see Lauritzen and Spiegelhalter, 1988), and the likelihood of different states in the affected child nodes updated. The ability of BBNs to perform bi-directional reasoning also provides an excellent diagnostic tool for identifying the most likely state of a parent node(s) leading to a particular state in a child node of interest. For example, if each of the four classes of community can be considered a proxy for the entire biodiversity within it, then a user could interrogate the BBN to find the combination of geographic, topographic, and environmental settings most likely to be associated with high survival of each community type in turn. Such information could then be included in planning for the sighting of marine protected areas that would have a minimal susceptibility to coral bleaching impacts.

Results

Figure 7 displays the BBN identified from the dependency analysis. As expected, the state of the heat stress variable max3day did have a dependency on cost100, while it in turn provided a level of dependency for bleach and dead. Community, along with its enforced dependency on habitat, also had some level of dependency on cost100, potentially reflecting how GBR coral community types “track” water motion and wave impact gradients to a large extent (Done 1982). The lack of a directed link between community and bleach is suggestive of conditional independence between these variables. This does not imply that they are independent of each other, rather that once the state of max3day is known, knowledge of the state of community does not change the likely state of bleaching. This however is not the case for the community and dead variables, because their direct linkage suggests that knowledge of community is needed to quantify the progression from bleach dead. The linkage between max3day and dead also confirms the general wisdom that the progression from bleach dead is conditional on extended exposure to high SST (i.e. as captured by the proxy max3day).
Fig. 7

BBN for the prediction of coral mortality, which includes “evidence” nodes to describe both the thermal environment and coral reef characteristics. Note that when a BBN is actually used, the likelihood (i.e. probability) of an evidence node taking a particular state is entered (e.g. based on field observations). The effects of the evidence are then propagated throughout the dependence-structured network via a probabilistic inference algorithm and the likelihood of different states in the affected child nodes updated

The sensitivity analysis highlighted how much the mean belief value of the dead node could be influenced by a single finding at each of the other nodes in the network. For both the high and low states of dead, the bleach and max3day nodal variables were the most influential components within the network (Fig. 8). Neither link was unexpected: the first because the dead field estimate referred to corals that had been judged to have died as a result of bleaching; the second because the max3day indicator was chosen in the first place because of its correlation with the presence or absence of bleaching (Berkelmans et al.2004 this issue). Community provided the next highest level of influence. Interestingly, the low state for the dead variable was more sensitive to the community variable than the high state. The importance of this subtle observation is given meaning by the results in the next section. Finally, the dead variable was relatively insensitive to cost100 and habitat, their influence being propagated to dead through their larger effects on max3day and community, as described above.
Fig. 8a,b

Sensitivity of (a) high dead coral cover, and (b) low dead coral cover, to changes in individual nodes of the BBN in Fig. 7. The bars represent the range of variation observed in the dead nodal variable when values for the states in each node on the y-axis were varied over their possible ranges and all other nodes were held constant at their most likely value

Bayesian network predictions

The BBN developed in Fig. 7 was tested for its decision-support capabilities. For the 150 sites classified by Done et al. (2003), the BBN correctly assigned 106 (71%) to their observed coral mortality class (Table 4). There was essentially equal predictive ability for low, medium, and high levels of coral mortality.
Table 4

Observed and predicted coral mortality for the 150 survey sites. Predictions are based on the BBN shown in Fig. 7 that included variables to characterize both the thermal environment and coral reef characteristics

Predicted Coral Mortality

Observed

Predicitive Rate

Low

Medium

High

26

7

3

Low

26/36=0.72

11

46

9

Medium

46/66=0.70

1

13

34

High

34/48=0.71

To test the loss of utility that would result in the absence of community information, we developed a new BBN in which the dead variable had no dependency on community (Fig. 9). As summarized in Table 5, for the new BBN, only 91/150 sites (predictive rate 61%) were correctly assigned to their observed coral mortality class. Interestingly, the majority of the loss in predictive capacity was in relation to the low coral mortality class (36% compared with 72% when the community node was included). This represents a 10% loss in predictive capability in situations where the objective was to identify areas with low coral mortality potential.
Fig. 9

BBN for the prediction of coral mortality, which includes ‘evidence’ nodes that only describe the thermal environment

Table 5

Observed and predicted coral mortality for the 150 survey sites. Predictions are based on the BBN shown in Fig. 9 that included variables for only the thermal environment

Predicted Coral Mortality

Observed

Predicitive Rate

Low

Medium

High

13

18

5

Low

13/36=0.36

6

46

14

Medium

46/66=0.70

1

15

32

High

32/48=0.67

Perhaps of most importance are the 15 occasions when Done et al. (2003) observed low mortality in conjunction with medium-high heat stress conditions (i.e. Type C sites in Fig. 1). In these instances, the BBN in Fig. 7 correctly predicted nine of them, whereas in Fig. 9 none were predicted. On further inspection, community type 3 (i.e. KM3) was found to be dominant when the BBN in Fig. 7 correctly predicted low mortality given medium-high heat stress conditions. KM3 was a low diversity Acorpora/Faviid community of reef flats and shallow slopes (see Table 2b). The result adds further support to the idea that intertidal or shallow subtidal reef flat sites - by virtue of shallow depth and periodic exposure to air during low tides – may be relatively more sun-hardened and/or heat-hardened than reef slope sites (see for example, Brown et al. 2002). These results clearly highlight the potential for differential mortality responses to heating stress depending on the resident community type. Moreover, the sensitivity results did not strongly allude to this finding, suggesting caution to empirical approaches (e.g. regression type analyses) that seek to judge the “significance” of information variables based solely on their ability to explain the global variance. Many of the subtleties within the system are conditional responses. BBNs provide an excellent means of codifying and working with these conditional-type responses.

Reconstructing high from low-resolution heat-stress maps, using learnt relationships

The 1998 relationship learned between max3day (50 km) and max3day (1 km), given the supporting evidence of cost100 and PCA, did provide a promising basis for extrapolative prediction in 2002. Fig. 10 displays the BBN that was developed from the 1998 test data. When the BBN was applied to predicting the 2002 heat stress at 1-km resolution (i.e. using cost100, PCA, and the 2002 max3day (50-km) map), its overall predictive success was 68% (Table 6), with essentially equal predictive ability across the low, medium, and high states. Fig. 11 provides insight into the sensitivity of the predictions of max3day (1 km) to changes in the other nodes of the BBN in Fig. 10. As expected, variation in the max3day (50-km) node resulted in the largest potential variation for the max3day (1-km) node. The influence of the PCA and cost100 nodes, however, was also significant. It is important to note that the fine-scale information provided by PCA and cost100 are different in nature. The effect of cost100 would seemingly be based on the physics of the potential deep-water cooling mechanism. The effect of PCA on the other hand, was not based on physics, but rather on simple precedent. The PCA categories range from cooler to hotter, based on a decadal average of maximum summertime temperatures (1990–2000, excluding 1998). Neither the PCA scores nor the categories imply anything about the mechanisms that caused them: i.e. the locally and annually varying combinations of weather and oceanography. PCA improves the prediction at the 1-km scale simply by “learning from the past”: i.e. by giving weight to the evidence of prior geographic patterns of SST that have been statistically smoothed over a decade.
Fig. 10

BBN for the prediction of the heat stress indicator max3day for a 1-km pixel size, given “evidence” from the equivalent 50-kmversion and the PCA and cost100 indicator variables. Conditional relationships were “learned” from the thermal conditions experienced by 1,994 reefs during the summer of 1998

Table 6

Observed and predicted values for the max3day (1 km) indicator for the thermal conditions experienced during the summer of 2002. Predictions are based on the BBN shown in Fig.10 for which the conditional relationships were “learnt” from the thermal conditions experienced by 1,994 reefs during the summer of 1998

Predicted Coral Mortality

Observed

Predicitive Rate

Low

Medium

High

452

154

73

Low

452/679=0.67

123

415

96

Medium

415/634=0.65

44

148

489

High

489/681=0.72

Fig. 11a,b

Sensitivity of (a) high max3day (1 km), and (b) low max3day (1 km), to changes in individual nodes of the BBN in Fig. 10. The bars represent the range of variation observed in the max3day (1-km) nodal variable when values for the states in each node on the y-axis were varied over their possible ranges and all other nodes were held constant at their most likely value

We now consider the case in which no heat stress information exists at the 1-km scale. If we substitute the “submodel” of Fig. 10 for the previously known max3day (1-km) node in our original bleaching BBN model (Fig. 7), we get the extended model shown in Fig. 12, whose predictive ability is summarized in Table 7. In this case, 89/150 (predictive rate 59%) sites were correctly assigned to their observed coral mortality class; a loss of 12% predictive capability compared to using the known values of max3day (1 km). Here, the “low” coral mortality class is the least successfully predicted (56%). The approach still appears useful however, especially in identifying sites with medium and high coral mortality.
Fig. 12

BBN in which the downscaling “submodel” shown in Fig. 10 is substituted for the previously known max3day (1-km) indicator. All other relationships are as identified for the BBN in Fig. 7

Table 7

Observed and predicted coral mortality for the 150 survey sites. Predictions are based the BBN shown in Fig. 12 that included the downscaling “submodel” to provide characterization of the thermal environment

Predicted Coral Mortality

Observed

Predicitive Rate

Low

Medium

High

20

12

4

Low

20/36=0.56

9

41

16

Medium

41/66=0.70

0

20

28

High

28/48=0.67

Discussion

Through our coral bleaching case study, we have been able to demonstrate the potential for remotely sensed observations (in this case SST measurements) to act as information channels in BBNs. In particular, we have highlighted the benefit of “value-adding” to remotely sensed and other spatial data sets through the creation of proxy indicators. For example, the proxy heat stress indicator max3day (1-km resolution) was found to provide the bulk of the predictive power for the BBN. While this finding simply reaffirmed prior conventional wisdom, the inclusion of a “precedent” proxy for summertime sea temperature (PCA), and a “mechanistic” proxy for cooling (cost100) improved our efforts at predictive description. The BBN also showed us that cost100 provided a spatial linkage to the most likely coral community type, not just to the heat stress indicator. When the heat stress and community indicators were combined, our ability to predict coral-bleaching related mortality was improved beyond that provided by the heat stress indicator alone. This alerted us to the potential for differential mortality responses to heating stress depending on the resident community type.

The results from this study have particular importance for the process of planning the configuration of a marine reserve network that would seek to minimize or spread the risk of coral bleaching impacts. In such situations, it would appear that it is clearly advantageous to know the endemic coral community in an area. For areas in which this information is lacking, extrapolation from known zonation patterns of coral communities across reefs and reef tracts (e.g. Done 1982 for the central GBR) could prove beneficial.

We were encouraged by the utility that we achieved using exceedingly simple proxy indicators (e.g. cost100, PCA) in place of detailed mechanistic descriptions of coral reef environments. It suggests that there will be value in developing additional indicators that provide a more refined characterization of the local oceanography and associated thermal environment. This should improve the performance of future BBNs in predicting the stress and recovery responses of coral reefs at a range of space-time scales. Our success in using the BBN framework to reconstruct predictive detail at 1-km resolution was also noteworthy. It suggests that it may be possible to develop a means of replicating the predictive capacity of our work for the majority of coral reef areas worldwide for which remotely sensed SST measurements are only collected or processed at the 50-km scale. It would be remiss however not to mention that this downscaling methodology is heavily reliant on the availability of detailed physical information (i.e. bathymetry, current patterns) which may not be available everywhere.

On a more technical note, the ability to learn robust relations from data-driven methods will clearly be best when large amounts of information (i.e. supporting evidence) is available. However the levels of inference we gained from some of the above analysis were very useful despite having been learned from a relatively small survey sample. One reason for this is because the informative content of each data point was strengthened by our decision to explicitly target thermal conditions of interest. Moreover, the learning algorithm that we utilized to search for structural dependencies in our data sets (Cheng et al. 2002) was able to accept informed (“expert”) guidance on the initial structure as a Bayesian “prior belief,” thereby freeing up the information content of the data to aid in the discovery of weaker dependency signals. While our initial results are encouraging, the next step will be to evaluate our learned dependencies against an independent data set. This is the subject of on-going research and will be reported elsewhere.

Conclusion

In this paper, we drew attention to an approach and ways of thinking that on the one hand provided very helpful insights to us, and on the other, have potential to facilitate the transfer of information and knowledge into the decision-making domain of coral reef policy-makers and managers. Through our case study, we demonstrated how the Bayesian paradigm, and in particular the decision-support capabilities provided by Bayesian belief networks (BBN) can assist in this endeavor.

The BBN developed for this study was shown to accept all the major elements of our understanding of large-scale bleaching on the Great Barrier Reef – remotely sensed and in situ data, information, knowledge, and expert opinion – and fuse them into a framework that allowed us to explore the extent to which this eclectic mix could provide effective (and transparent) decision support in the task of correctly identifying those reefs which would be at the lowest risk of bleaching and subsequent coral mortality.

The level of understanding gained from our study confirms that the decision-support capabilities of BBNs are not necessarily limited by the need for scientists to understand and account for all mechanistic detail. This is because data gaps and uncertainties, in particular with regard to the inter-linkages of the BBN, are quantified as conditional probabilistic statements of relationships. Indeed, in our study, the level of descriptive complexity (i.e. dependency structure) for the bleaching BBN was learned from the information content of the available data (i.e. by incorporating the experience of past events and spatial relations).

The flexibility provided by BBNs also means that when new information becomes available, it will be an easy task for it to be incorporated, with only the conditional probabilities of the affected variables requiring re-evaluation. For complex adaptive systems like coral ecosystems, this is important since we are continually going to experience surprises in the magnitude (and potential type) of stress and recovery responses. Unlike methods that require us to continually throw away and start with a clean sheet, the BBN learning process allows us to build in insights gained through surprises or mistakes. This is a distinct benefit, since given the right perspective on time, these surprises almost always end up being our most valuable sources of information and experience.

Acknowledgements

We thank the following colleagues who have contributed to this work: Emre Turak and Mary Wakeford for assisting Terry Done with the bleaching assessments; Glenn De’ath and Ray Berkelmans for allowing us access to max3day prior to publication; Glenn De’ath for assistance in defining coral communities; Stuart Kininmonth and Steve Edgar for development of the GIS; Mike Mahoney for providing the SST data to enable the development of various SST indices in the GIS; Craig Steinberg for unpublished modeled current data that allowed us to develop the proxy cost100. The manuscript also benefited from the comments of two anonymous reviewers.

Copyright information

© Springer-Verlag 2004