Learning to predict large-scale coral bleaching from past events: A Bayesian approach using remotely sensed data, in-situ data, and environmental proxies
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- Wooldridge, S. & Done, T. Coral Reefs (2004) 23: 96. doi:10.1007/s00338-003-0361-y
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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.
KeywordsCoral bleachingBayesian belief networksRemotely-sensed SSTGreat Barrier Reef
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
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
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).
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)
Mid-shelf and outer-shelf reefs
Reef flats and slopes exposed to the prevailing seas from SE and SW quadrants
Reef flats and slopes and patches on and adjacent to sandy areas enclosed within the arc of the outer slope
Reef flats and slopes on the outer edge of reefs with a broadly NE and NW aspect
Reef flats and slopes forming die edges of between-reef channels that are tens of metres across
Reef flats and slopes, regardless of compass aspect
(b) Coral Communities
“Types” of coral communities-this study
Coral communities —Done 1982
‘Classes” of Coral Communities—Done 1982
Reef slopes — all habitats of offshore reefs
6. Acropora palifera/Porites,
II-’semi-exposed to sheltered’
8. Porites “massive/branching”
Reef slopes - all habitats of offshore reefs
II- ‘semi-exposed to sheltered”
10. Acropora ‘staghorn”
11. Acropora ‘tabulate/branching”
12. Acropora “tabulate”
Reef flat margins — all habitats of offshore reefs
1. Acropora palifera/humilis —
A. palmerae variant
2. Acropora palifera/humilis —
A. hyacinthus variant
3.Acropora palifera/humilis —
A. digitifera variant
All habitats - inshore fringing reefs
13. Acropora splendida/divaricata
III - “sheltered”
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
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.
Maximum heat stress (1-km resolution)
Maximum heat stress (50-km resolution)
An exploratory Bayesian analysis
Summary description of the proxy indicator variables used in the dependency analysis
Proxy Indicator Variable
Cost-weighted distance from the 100 m isobath
Classified habitat class
Classified coral community types
Maximum three-day run of summer SST (2002)
Classified bleaching impact
Classified coral mortality
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 (child∣parent1, 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.
Bayesian network predictions
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 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
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
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 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
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.
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.
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.