The ocean is beneficial for societal wealth and human development. The oceans offer access to food, materials, energy, and recreational opportunities. Many states take (and took) initiatives to master their access to marine resources; now often under a “blue” catch-word [a]: “The 'Blue Economy' concept has attracted much interest in international fora and become a key to development strategies of international organizations. This cross-cutting initiative aims to provide global, regional and national impact to increase food security, improve nutrition, reduce poverty of coastal and riparian communities and support sustainable management of aquatic resources.”
It is likely that seas and oceans, even more than today, will be a theatre of competing economic interests. Already today, the convenient availability of ocean resources has put high pressures on the health of the ocean, e.g.: overfishing shifts balances of ecosystems, pollution trough extraction industries threats regional seas, marine litter spoils recreation, plastic threatens marine life along the entire food chain, or alterations of coastal zones destroy unique habitats. The risk is high that these pressures increase when more “blue economy strategies” get implemented. In that context, an index to describe the overall ‘health of the ocean’ in a standardized manner would be much needed and could be a very useful management tool.
Drawing on experiences in coastal zone management, comprehensive assessments are emerging, which consider a composite of oceanic features that influence societal wealth and human development. The wealth of marine information that is available nowadays through a multitude of studies may be incomplete, but a tentative assessment of global ocean-health issues is possible. Against this backdrop, proposing comprehensive ocean-health index  and making it available [b] was a very important step forward towards a sustainable human use of the ocean; although some may consider this step as “bold” or even “too bold”.
Ten amalgamated assets
The ocean-health index amalgamates ten societal assets [c] undertaking one composite assessment of reference values, current status and future status. The ten assets were selected to cover a wide range of ecological, social, and economic benefits for a wide range of “use cases”. The score of the ocean-health index, a single number, shall describe the state of the human-ocean system as a composite-asset. The main assumption, implicit to the index, is that a combination of the ten assets should be preserved for any healthy human-ocean system, although the combination may vary regionally and in time.
The ocean-health index is presented annually at country/regional level and at global level. For 2012 and 2013, the score of the ocean-health index was estimated to be a modest 65 of 100 when averaged at the global level. The score of individuate countries varies between 41 and 94; and countries of very different natural and economic setting have the same score like Norway and Netherlands (74) compared to Iceland that scores 58.
The score for the ocean-health index is calculated as the weighted arithmetical average of the scores for the ten assets on which the index is built. Selecting these assets, identifying indicators describing them, gathering data measuring the indicators is a tedious and complex undertaking, which in itself gives ample space for biases, nuanced choices or simple errors. Improving the ocean-health index is subject of research and study that, by no means, renders the index meaningless, because it provides a means for global benchmarking and comparison that otherwise would be missing.
Compared to addressing possible defects “of substance” of the ocean-health index, it seems ‘picky’ to question the use of a “weighted arithmetical average” to calculate the score of the ocean-health index. Nevertheless that was done recently , for very good reasons, and with lessons that may serve as examples also for other index that calculate a score for a set of assets.
An innocent average ?
The mathematics of a “weighted arithmetical average” that is used to calculate the ocean-health index looks innocent and non-problematic.
An “arithmetical average” of single marks gives each mark the same impact on the composite mark. That makes good sense if a feature is marked several times, a set of measurements, a sample, is obtained, and thus the elements in the sample are belonging to the same kind but vary randomly. Using weights is a simple and transparent approach to set preferences between marks for features of similar kind, i.e. to account for some non-random variation within a sample of “features of about the same kind”.
Thus, in face of the intrinsic complexity to assess in a composite context the different assets that are underpinning the ocean-health index, taking an approach of “one asset one vote”, i.e. arithmetical average, looks like a fair, “democratic” first choice. Furthermore, giving different assets different weights looks like a fair option to reflect social or political choices without excluding a “minority asset”. Nevertheless, just these simple first-hand choices are not innocent but set a rather radical “normative frame”  for managing a set of “assets” by means of a index, which may limit the usefulness of the index.
Using an “arithmetical average” to obtain a score for a set of assets implies a paramount assumption, namely that “unlimited substitution possibilities” exist among these assets to obtain the same score. In that context, “substitution” means that under-performance for one asset can be balanced by better-performance for another asset; “unlimited” means that under-performance for one asset is not limited by a lower boundary; and “possibility” means that better-performance for any asset may balance under-performance of any asset. These assumptions are quite radical, indeed.
Using a “weighted arithmetical average” does not alter the assumption, although it modifies the “cost” of the substitution; i.e. performance for an asset with low weight has to improve much to balance a minor drop of performance of an asset with a high weight.
A radical “normative frame” ?
To perceive how radical is the assumption of “unlimited substitution possibilities among various assets”, one may assume: (1) a shopping list of ten items for the dinner table, (2) getting these items in different quality or quantity, but so that (3) the average quality of the dinner is the same. Evidently, a good starter may make good for a bad desert, or a good wine (or beer) compensates for…; but “unlimited substitution possibilities among the various parts of the dinner”? Common sense tells that this may work, indeed, but at best for a “below-standard dinner”.
|from: MARUM - Center for Marine Environmental Sciences |
(distributed via imaggeo.egu.eu)
Evidently, “unlimited substitution possibilities among various assets” is a framework for “a manager’s dream”. Such a framework maximises the number of operational alternatives to amalgamate assets although respecting social choices of different assets through their weighting.
However, “unlimited substitution possibilities among various assets” is an exceptional case. It is ”the real-world’s manager’s headache” that amalgamating assets is limited by the substitution potential among them. The substitution potential may be limited for ecological, technical or social preferences. Considering the ten single assets that are amalgamated into the ocean-health index, it seems possible that they substitute each other to some degree, but it is very problematic management guidance to assume that they substitute each other fully.
Strong or weak sustainability ?
Extremes in degree of substitution possibilities between assets is summarized in two alternative concepts, of either “strong sustainability” or “weak sustainability”. The former requires keeping all assets above critical levels, thus avoiding any substitution between them. Under the concept of “weak sustainability” substitution between assets is unconstrained and can be done without any limits.
That latter concept of “unconstrained substitution” is applied for the ocean-health index by the choice of the mathematical formulation how the average score of the ocean-health index is calculated ; namely using a weighted arithmetic mean.
The assumption, which is implicit to the mathematics, namely “unconstrained or unlimited substitution”, is unrealistic and may misled. However, it goes without saying that experienced managers of marine resources would be aware of limitations to substitution of assets, although implementing that awareness for a set of assets in a competitive environment is not only an intellectual challenge.
|Border between open sea water and a plum |
from the Mzymta river (Sochi, Russia)
from: Alexander Polukhin
(distributed via imaggeo.egu.eu)
Obviously, intermediate levels of substitution may be achieved for many real-world situations and their description by means of an index. And evidently, for many real-world situations it will be difficult to determine “what are boundaries to substitution?” Manifestly, any intermediate level of substitution for assets underpinning the ocean-health index will depend on the specific ecological-human intersections of the respective human-ocean system. Whatever is obvious, evident or manifest, it will be hard and tedious work to narrow the range of substitution possibilities, and in some circumstances “strong sustainability” should be applied to guide management choices, simply.
The mathematics to describe “intermediate levels of substitution” are available. Likewise the tools are available to study implications of having chosen a specific mathematical method to describe “intermediate levels of substitution”. They are used, for example, in social choice theory [d]. Aggregation of individual asset with constraint or limited substitution into a composite scores can be described using ‘generalized averages’ [e]; with arithmetic, geometric or harmonic average as special cases of the ‘generalized averages’.
Composite averaging procedures and intermediate level of substitution
Choices of limited substitution possibilities for the various assets of the ocean-health index can be made  applying state of the art knowledge on natural resources and ecosystem assessment, which are reflecting the state of the human-ocean system, and using appropriate mathematics, i.e. specific functional forms (“functions of functions”) [f].
The mathematics for calculating the index can get increasingly composite by working in a nested manner, using generalized means, applying variable setting of substitution with constraints on the overall score for the less-performing assets, and fixing “hard” lower boundaries.
Evidently, such kind of “composite averaging procedure” lacks the simplicity of the arithmetical average. The “composite averaging procedure” is more like an elaborated model of the substitution possibilities, which has to be analysed with care; not only for his non-linear behaviour.
Notwithstanding the complexity, such a model could capture our best understanding of the functioning of the ocean-human intersections though appropriate mathematics. As such it may be a very useful research tool.
However, the complexity of the model may be considered as much too high to abandon the “weighted arithmetical average” because of its relative transparency for many users. Thus for management environments the “weighted arithmetical average” may be preferred.
Ocean-health index with intermediate level of substitution
Recalculating the ocean-heath index with a modified methodology to calculate the average score , showed a considerable dependence of the ocean-health index on the choices for the substitution possibilities including substantial swings of countries between camps of “well-performing countries” and “under-performing countries”.
|The English Channel in Cap Blanc-Nez; |
above the two ships a brown pollution layer;
probably containing NO2 and aerosols.
from: Alexis Merlaud (distributed via imaggeo.egu.eu)
The bulk result of the study  is that the global ocean-health index decreases by 20%; namely from a score of 65 of 100 to the score of 52 of 100 if the “weighted arithmetical average” is replaced by a revised methodology limiting substitution among assets. The revised index reduces less-realistic possibilities for offsetting poorer performances in certain assets by better performances in other assets. The drop of the global ocean-health index is important, and possibly many decision makers, who would find a score of 65 of 100 “still tolerable” - two good for one bad -, would modify that view for a score of 52 of 100.
Even more striking is the finding :“...when we turn to the assessment of individual countries. Countries with an unbalanced performance across the assets significantly deteriorate in the ranking compared to countries with a balanced performance. For example, Russia and Greenland fall in the ranking for 2013 by about 107 and 118 places (out of 220) respectively, while Indonesia and Peru improve by about 78 and 88 places respectively.” Similar striking changes are observed regarding the assessment of change over time, for one out of four countries the direction of change is inverted.
What is the lesson to draw?
Th ocean-health index is useful because of the limitations of choices that were made when designing it. The challenge to describe a set of assets through a single index drives insights into the human-ecological intersections of the human-ocean system, including the issue of appropriate mathematical description.
A first insight to keep:
Setting up an ocean-health index  was a very relevant endeavour, and is a lasting contribution to the management of the human-ocean system. An ocean-health index could be a tool for comparison of national and regional policies, benchmarking, and qualification of development options, which is much needed to manage global commons like the ocean. Implications of the (simple) mathematics to calculate the ocean-health index have been analysed .
The result of the study indicates that the mathematical method chosen for calculating the average is causing bias of the index. The method to calculate the score of the index by “weighted arithmetical average”, makes the index insensitivity to less-appropriate choices to substitute assets for which performance is low by better-performing assets. This feature of the index limits the use of index. The possibility of unconstrained mutual substitution between assets within the composite score requires adjustment. Without such adjustment : “policy assessment and advice based on an index with unlimited substitution possibilities could result in (a) certifying a healthy human-ocean system for countries that in reality neglect important aspects of ocean-health and (b) identifying development trajectories as sustainable although this is actually not the case.”
A second insight to keep:
The assessment of the various oceanic features relevant for societal wealth and human development is improved, if substitution possibilities among different assets are constrained. Evidently, the substitution of different assets is a societal endeavour. It requires knowledge, social choices and norms and particular the latter may evolve and vary among societies.
Nevertheless, any substitution possibility should be limited and confined by boundaries of the elasticity of the ocean system, if we know the ‘elasticity’ otherwise the “strong sustainability concept” or the “precautionary principle” should be applied. For being practical, the retained substitution possibilities should provide for some elasticity to have a margin for management decisions - not everything goes, not all is forbidden – to render the ocean-health index a tool with operational value.
A third insight to keep:
Furthering the analysis of suitable substitution of assets and how to describe the substitution process in mathematical terms is needed to properly evaluate benefits, risks and development options of the ocean-human system.
For the best or the worth, a common and robust ocean-health index is a much welcomed management tool, and possibly the ocean-health index will be part of any mature ‘blue economy strategy’. Thus, it is important to design the index in a manner that is sound and practical. The alternative would be to manage all assets one-by-one using the “strong sustainability concept”, what possibly would end in a political process to retain on a case-by-case only those assets that are considered most relevant. In that situation any comparison of national and regional policies, benchmarking, and qualification of development options would be far more difficult.
Thus, one composite index has a strong appeal. However, attention should be given to the complexity of the averaging procedure, which if too complex or perceived as too complex would hamper application of the index. To recall, the attractiveness of calculating the ocean-health index by a weighted arithmetical average is the simplicity of the procedure that is understandable for many.
Possibly a two tiers approach may provide a useful compromise. Tentatively, such a compromise could be: (i) apply the “strong sustainability concept” to identify assets that either match this concept or fail, (ii) calculate the score of the ocean-health index for both subsets, (iii) calculate the arithmetical average of both sub-scores (weighted by the number of assets in each set) to get the score of the ocean-health index, and (iv) present this score with the scores for the sub-indexes as lower and upper bound.
How to generalize this experience? What has been discussed above for the ocean-health index applies "mutatis mutandis" to any index that gives an average composite score of several assets that can substitute each other only partially.
[c] The single assets of the ocean-health index are: (1) Artisanal Fishing Opportunities, (2) Biodiversity i.e. species and habitats, (3) Coastal Protection, (4) Carbon Storage, (5) Clean Waters, (6) Food Provision i.e. fisheries and aquaculture, (7) Coastal Livelihoods & Coastal Economics, (8) Natural Products, (9) Sense of Place i.e. iconic species’ and special places, and (10) Tourism & Recreation [x].
 An index to assess the health and benefits of the global ocean (2012). Benjamin S. Halpern, Catherine Longo, Darren Hardy, Karen L. McLeod, Jameal F. Samhouri, Steven K. Katona, Kristin Kleisner, Sarah E. Lester, Jennifer O’Leary, Marla Ranelletti, Andrew A. Rosenberg, Courtney Scarborough, Elizabeth R. Selig, Benjamin D. Best, Daniel R. Brumbaugh, F. Stuart Chapin, Larry B. Crowder, Kendra L. Daly, Scott C. Doney, Cristiane Elfes, Michael J. Fogarty, Steven D. Gaines, Kelsey I. Jacobsen, Leah Bunce Karrer, Heather M. Leslie et al., Nature 488. doi:10.1038/nature11397
 How healthy is the human-ocean system? (2014). Wilfried Rickels, Martin F Quaas and Martin Visbeck. Environmental Research Letters Vol. 9(4). doi:10.1088/1748-9326/9/4/044013