domain: spi shs spi.other

text:
Andreas Hein

Makoto

Juliette Brun

ICED A CONCEPTUAL FRAMEWORK FOR BREAKTHROUGH TECHNOLOGIES

Keywords: Technology, Systems Engineering (SE), Design theory, Breakthrough technology, Radical innovation

Breakthrough technologies introduce a radically new capability or a drastic performance improvement. However, the existing engineering design literature does not specifically pay attention to them. In this paper, we present a conceptual framework for breakthrough technologies, aiming for a more detailed characterization of breakthrough technologies. First, based on a literature survey, we reflect on the relationship between breakthrough technology and innovation. In addition, we explore the relationship between breakthrough technologies at the component and system level. Next, we propose a conceptual framework with dimensions in which breakthroughs may occur and the corresponding expansion of concepts and knowledge, drawing from C-K theory. We subsequently apply the framework to the case of a laser sail-propelled interstellar probe. We conclude that the relationship between component and system-level breakthrough technologies requires further exploration. Furthermore, the coupling between the breakthrough technology and market breakthrough in the form of a new business model seems interesting for future work.

INTRODUCTION

"Breakthrough technology" literally means a technology that has broken through some kind of obstacle, barrier, or may indicate a sudden advance (Merriam-Webster Inc., 2004). It has previously been defined as a technology that introduces a "radically new capability or a performance improvement of at least an order of magnitude" [START_REF] Hein | Breakthrough technologies: principle feasibility debates[END_REF]. Similar notions have been proposed in the technology management literature such as "game changer" [START_REF] Rice | Managing discontinuous innovation[END_REF], discontinuous innovation [START_REF] Rice | Managing discontinuous innovation[END_REF], breakthrough innovation [START_REF] O'connor | A comprehensive model of uncertainty associated with radical innovation[END_REF], and technological breakthrough [START_REF] Chandy | The incumbent's curse? Incumbency, size, and radical product innovation[END_REF]. Historical examples include the Wright Brothers airplane (controlled, sustained heavier-than-air flight) and the transistor (orders of magnitude smaller size and energy consumption than vacuum tubes). Each of these technologies has either introduced an unprecedented capability (Wright Brothers airplane) or an at least order of magnitude improvement in performance (transistor). Today, the Google search engine (machine-powered search) [START_REF] Masters | Zero to one: notes on start ups, or how to build the future[END_REF] and self-driving cars [START_REF] Teller | Google X Head on Moonshots: 10X Is Easier Than 10 Percent[END_REF] are prominent examples. Breakthrough technologies or their equivalents are considered key for sustained competitive advantage [START_REF] O'connor | A comprehensive model of uncertainty associated with radical innovation[END_REF]. Breakthrough technologies are at the origin of radical innovations, which transform or create a new market [START_REF] Garcia | A critical look at technological innovation typology and innovativeness terminology: a literature review[END_REF][START_REF] Rice | Managing discontinuous innovation[END_REF].

Despite their importance, the engineering design literature does not seem to have paid much attention to breakthrough technologies. One reason might be that the link between engineering design and innovation remains in general underexplored [START_REF] Isaksson | Perspectives on Innovation: The Role of Engineering Design[END_REF]. The existing engineering design literature is primarily focused on how technologies, for example, in the form of working principles can be used in a new product [START_REF] Pahl | Engineering design: a systematic approach[END_REF]. Furthermore, the literature deals with how technologies can be integrated into the architecture of an existing product [START_REF] Smaling | Assessing risks and opportunities of technology infusion in system design[END_REF][START_REF] Suh | Technology infusion for complex systems: A framework and case study[END_REF], the maturity of technologies [START_REF] Fragola | A practical top-down approach to assess programmatic risk for projects with low-TRL elements[END_REF][START_REF] Mankins | Technology readiness levels[END_REF][START_REF] Sauser | From TRL to SRL: The concept of systems readiness levels[END_REF], and predicting the future performance of technologies in order to identify promising system architectures [START_REF] Knoll | A concurrent design approach for model-based technology roadmapping[END_REF]. No specific distinction between types of technologies is presented, except for its maturity (Technology Readiness Levels) and whether or not fundamentally different working principles are used (creative design vs. routine design). However, the technology management literature has recognized for a while that the type of technological innovation has important implications on which new product development process to choose [START_REF] Rice | Managing discontinuous innovation[END_REF][START_REF] Song | Critical development activities for really new versus incremental products[END_REF]. [START_REF] Rice | Managing discontinuous innovation[END_REF] have argued that processes for incremental innovation are ill-adapted to radical innovation projects, making them more likely to be canceled. One of the reasons is the much higher uncertainty related to developing breakthrough technologies and finding a market [START_REF] O'connor | A comprehensive model of uncertainty associated with radical innovation[END_REF][START_REF] Song | Critical development activities for really new versus incremental products[END_REF]. Based on this literature, we argue that breakthrough technologies need to be treated differently in engineering design than other technologies.

In this paper, we propose a conceptual framework for breakthrough technologies, in order to provide a basis for future engineering design methods, specifically aimed at the development of products or systems using breakthrough technologies. Section 2 reviews literature from different domains, where breakthrough technologies and related concepts have been discussed, section 3 introduces the conceptual framework, and section 4 presents an application of the framework to a case study.

LITERATURE REVIEW

Having argued for the importance of treating breakthrough technologies in engineering design, we propose to shed more light on the relationship between innovation categories and breakthrough technologies. How are innovation categories assigned to breakthrough technologies? In a first step, we clarify what we mean by "technology" and then discuss the meaning of "breakthrough". For this purpose, we consult the technology management, technology history, and sociology of technology literature and finish with the innovation management literature.

Technology management, sociology, and history

Our definition of breakthrough technology can be firmly grounded in the technology management literature. According to [START_REF] Iced Sahal | Patterns of technological innovation[END_REF], a technology is defined by its main function and its performance characteristics. An example would be the function "generate thrust" for aircraft engines, where a crucial performance characteristic is the thrust-to-weight ratio. He calls this definition of a technology the systems concept of technology. [START_REF] Iced Sahal | Patterns of technological innovation[END_REF] argues that this definition is most appropriate for describing intrinsic technology-related dynamics, expressed by key performance parameters. As performance is by definition a key characteristic of a breakthrough technology, we will use the systems concept of technology in the following. From this point of view, a breakthrough exhibits a new main function (new capability) or performance discontinuities. The systems concept of technology also seems to be compatible with the way technologies are treated in the engineering design literature.

Performance discontinuities have been described in the technology history and sociology of technology literature. More specifically, in his study of the jet engine, [START_REF] Constant | The origins of the turbojet revolution[END_REF] refers to the notion of "reverse salient". A reverse salient is caused by a component technology in a system that prevents the overall system to increase its performance. The propeller engine created a reverse salient for airplanes, preventing their evolution towards higher speeds and altitudes. A breakthrough occurs when a component technology removes the reverse salient. According to [START_REF] Hughes | Networks of power: electrification in Western society[END_REF], a reverse salient appears when a technological or socio-technological system is already on an evolutionary trajectory, on which its component technologies co-evolve (e.g. performance improvement of power plants and distribution network in an existing electrical network). However, we do not see an obstacle to using the notion of reverse salient for a system that is at the beginning of an evolutionary trajectory. Technological breakthroughs are associated with the beginning of an evolutionary trajectory [START_REF] Chandy | The incumbent's curse? Incumbency, size, and radical product innovation[END_REF]. For example, the Wright Brothers needed to develop a sufficiently lightweight internal combustion engine for their airplane to take off. An insufficient performance of this component technology is one reason why crewed heavier-than-air aircraft did not emerge earlier [START_REF] Chanute | Progress in Flying Machines[END_REF]. At the beginning of an evolutionary trajectory, a breakthrough in one or more component technologies leads to breakeven performance at a system level, for example, to qualify as controlled, sustained, heavier-than-air flight. To give another example, [START_REF] Rose | Controlled nuclear fusion: Status and outlook[END_REF] presents the case of fusion reactor development, where breakeven performance is linked to keeping the plasma stable over sufficient periods of time, in order to get more energy out of the reactor than has been put in.

An important conclusion from this stream of literature is that there is an important relationship between breakthroughs at the component technology and system level.

ICED

Innovation management

A breakthrough technology can be the basis of an innovation. In the following, we are particularly interested in the link between specific innovation categories and breakthrough technologies. Such categories are introduced in the innovation management literature, such as [START_REF] Chandy | Innovation typologies[END_REF], [START_REF] Garcia | A critical look at technological innovation typology and innovativeness terminology: a literature review[END_REF], [START_REF] Garcia | Types of Innovation[END_REF][START_REF] Kotsemir | Innovation concepts and typology-an evolutionary discussion[END_REF]. According to OECD (1991), innovation is "an iterative process initiated by the perception of a new market and/or new service opportunity for a technology-based invention which leads to development, production, and marketing tasks striving for the commercial success of the invention." This definition highlights two necessary ingredients of innovation: The invention linked to a technology and its commercial success.

These two elements of an invention appear consistently in existing innovation categorizations. Based on an extensive literature survey, [START_REF] Garcia | A critical look at technological innovation typology and innovativeness terminology: a literature review[END_REF] conclude that a common factor in existing innovation categorizations is that innovations are linked to different degrees of technological and/or marketing discontinuities. Incremental innovation implies minor discontinuities in one and/or the other. A radical innovation implies major discontinuities in both. It is an innovation that is based on a new technology and which drastically changes or creates a market. A really new innovation is between these two extremes and implies a major discontinuity in either technology or marketing. In light of this categorization, a breakthrough technology is a major discontinuity in technology. In case it leads to a minor discontinuity in marketing, it is a really new innovation. In case it leads to a major discontinuity in marketing, it is a radical innovation.

Furthermore, [START_REF] Rice | Managing discontinuous innovation[END_REF] characterize major technological discontinuities more specifically. They call a technology a game changer, if it has the potential of a (1) 5-10 times performance improvement compared to existing products, (2) to create a basis for 30-50% reduction in costs; or (3) to have new-to-the-world performance features. Game changers seem to be very close to our notion of breakthrough technology, although the values for performance improvement differ (5-10 times versus 10 times). [START_REF] Chandy | The incumbent's curse? Incumbency, size, and radical product innovation[END_REF] distinguish between a technological and market breakthrough. A technological breakthrough is the emergence of a new technology at the beginning of the technology S-curve, whereas a market breakthrough is a discontinuity in the benefits generated by the technology.

Table 1 summarizes which innovation categories are compatible with a breakthrough technology. Radical innovations and really new innovations might be based on a breakthrough technology. Incremental innovations are in general not linked to a breakthrough technology. From the reflection of the notion of breakthrough technology with the existing technology management and innovation literature, we draw the following conclusions:

-A "breakthrough" can happen at the component technology and system level: If it happens at a component technology level, it could lead to a breakeven or even a drastic performance improvement of the overall system. However, we can also imagine a case where component technologies that are individually not breakthrough technologies are combined to a system and the system exhibits the characteristics of a breakthrough technology. -Breakthrough technologies can be the basis for certain types of innovation: A breakthrough technology can be the basis for radical and really new innovations. A radical innovation combines a major technological discontinuity with a new market discontinuity. In a really new ICED innovation, the breakthrough technology introduces a major technological discontinuity, while the market discontinuity remains minor [START_REF] Garcia | A critical look at technological innovation typology and innovativeness terminology: a literature review[END_REF].

In order to develop engineering design methods specifically for breakthrough technologies, we need to further deepen our conceptual understanding of breakthrough technologies. For this purpose, we will present a conceptual framework for breakthrough technologies in the following section.

A CONCEPTUAL FRAMEWORK FOR BREAKTHROUGH TECHNOLOGIES

In the following, we present a conceptual framework for breakthrough technologies. We combine Concept-Knowledge (C-K) theory [START_REF] Hatchuel | A new approach of innovative Design: an introduction to CK theory[END_REF] and breakthrough dimensions based on [START_REF] Abernathy | Patterns of industrial innovation[END_REF]. Both integrate concepts from a variety of domains such as design science, innovation management, sociology of technology, technology management, and technology history. We select these two generic frameworks, as our aim is to integrate concepts from different streams in the literature. C-K theory is a widely cited theory of design. It distinguishes between concept and knowledge. A concept is an object for which the logical status of some of its propositions, for example, its existence, is unknown (neither true nor false). An example is an antibiotic without resistance. We do not know if such an antibiotic exists. Another example is a flying taxi. It is an object whose status is yet unknown in terms of its function, performance, etc. Knowledge encompasses propositions with a known truth value (either true or false). For example, we know that antibiotics exist or airplanes can cross the Atlantic. We use "concept" and "knowledge" in a rather informal way in the rest of the paper, where "concept" stands for a new conceptual idea and "knowledge" for different forms of knowledge or know how. We are primarily interested in categorizing novelties in terms of concepts and knowledge. We distinguish between four categories of novelty, shown in Table 2. These different levels of expansion in C or K allow for a more detailed distinction between cases where something new is created conceptually (a new design, a new function, etc.) or new knowledge is developed (gaining experience with a design, function, etc.). [START_REF] Hatchuel | A new approach of innovative Design: an introduction to CK theory[END_REF] ΔC-ΔK: New concept and major knowledge expansion (Example: cloud chamber) δC-δK: Minor concept and knowledge expansion δC-ΔK: Applied science -Existing concept but major knowledge expansion (Example: quartz watch) [START_REF] Hatchuel | A new approach of innovative Design: an introduction to CK theory[END_REF] We further derive a set of breakthrough dimensions from the literature. Dimensions from [START_REF] Abernathy | Patterns of industrial innovation[END_REF] are a technology's performance, usage in terms of operations, value for stakeholders in terms of "identification of an emerging need or a new way to meet an existing need", and the business model. These dimensions correspond to different dimensions of breakthroughs (technology and market breakthroughs). Some of these dimensions also exist in the engineering design literature such as usage [START_REF] Pahl | Engineering design: a systematic approach[END_REF] and value [START_REF] Crawley | Systems Architecture: Strategy and Product Development for Complex Systems[END_REF]. The business model links to the business literature [START_REF] Demil | Business model evolution: in search of dynamic consistency[END_REF][START_REF] Mcgrath | Business models: A discovery driven approach[END_REF][START_REF] Osterwalder | The business model ontology: A proposition in a design science approach[END_REF][START_REF] Teece | Business models, business strategy and innovation[END_REF]. Additionally, we add the dimension of engineering and physical principles, in order to account for the major technological discontinuity of a breakthrough technology [START_REF] Henderson | Architectural innovation: The reconfiguration of existing product technologies and the failure of established firms[END_REF]. This dimension also helps to distinguish a breakthrough technology from incremental improvements that can also lead to large increases in performance when accumulated [START_REF] Abernathy | Patterns of industrial innovation[END_REF].

We propose a matrix representation for the breakthrough technology framework. We construct this matrix by putting C and K expansions into columns and breakthrough dimensions into rows, as shown in Table 3. The first two rows are characteristics of a breakthrough technology and the last three characteristics of a market breakthrough. Combined, they are characteristics of a radical innovation. An entry under δC-δK indicates that only a minor discontinuity has occurred and the row criterion is not satisfied. ΔC-δK or δC-ΔK indicates that a major discontinuity has occurred but ICED whether or not it satisfies the row criterion has to be decided on a case to case basis. Finally, ΔC-ΔK is a major discontinuity and satisfies the row criterion. We use the Wright Flyer example in 1903 when the first controlled flights were executed. The Wright Brothers rigorously expanded knowledge about airplane design and combined component technologies to create a functioning airplane. Although some of the component technologies were inventions such as wing-warping for control, the bi-plane aircraft, airfoil, and internal combustion aircraft engines (Manly-Balzer engine in 1901) all existed prior to the Wright Flyer. Hence, in 1903 the Wright Flyer was a breakthrough technology, introducing the new capability of controlled, crewed, heavier-than-air flight. Nevertheless, no clear application of the technology existed at that point, which leaves the last three rows empty. Hence, we argue that the Wright Flyer in 1903 was a breakthrough technology, primarily due to the new capability it introduces but is not yet a radical innovation.

We also demonstrate that the matrix can be used for characterizing a (potential) breakthrough technology at different points in time. In 1909, the Wright Flyer was proposed as a military observation airplane. The result is shown in Table 4. A striking observation is that the application of the Wright Flyer as a military observation airplane was conceptually new, with little prior knowledge at the point of introduction. This led to a major knowledge expansions of how to use an airplane for this purpose. Only minor changes in new engineering and physical principles are observed, mainly focusing on incremental improvements in reliability. A major expansion of C and K occurs in terms of using an airplane for military observation. The Wright 1909 Military Flyer is the first airplane to satisfy the performance requirements for a military observation airplane. It thereby creates a new market for military observation airplanes with a new business model of selling them.

Radical innovation Breakthrough technology

ICED A remaining task is to define the notion of potential breakthrough technology, which hinges on the interpretation of "potential". For example, the first internal combustion engine was developed by Huygens in the 17th century but the engine fell apart after a few cycles [START_REF] Huygens | A New Motive Power by Means of Gunpowder and Air[END_REF]. Huygens somehow had the propulsion of vehicles in mind as an objective. However, neither a vehicle was developed nor was one conceptualized [START_REF] Huygens | A New Motive Power by Means of Gunpowder and Air[END_REF]. Hence, we feel that it does not qualify as a potential breakthrough technology for the reason that it was not intended to create a breakthrough. Hence, we can formulate minimal conditions for a technology qualifying as a potential breakthrough technology:

-A clear formulation of where the technology might cause a potential breakthrough (for which higher-level system, market etc.), similar to the articulation that a technology will be a "game changer" [START_REF] Rice | Managing discontinuous innovation[END_REF]); -A reasonable extrapolation of performance values from the prototype indicates that the breakthrough is likely to occur. Another challenge is the distinction between different hierarchical levels (system or component level). This distinction is often neglected in the technology management and innovation literature but is important in engineering design. Is the jet airplane (system) the breakthrough technology or is it the jet engine (component technology)? We argue that breakthrough technologies can indeed emerge at different hierarchical levels. For example, the jet engine led to immediate improvements in thrust to weight ratios of about an order of magnitude. This improvement led to the elimination of the reverse salient that existed in airplanes in terms of flight altitude and velocity. On the other hand, jet airplanes themselves lead to drastic performance improvements that opened up new areas of activity (stratospheric flight) that would count as breakthroughs. However, as the case study in Section 4 shows, a combination of non-breakthrough component technologies can lead to a breakthrough on the system level and vice versa.

To summarize, a breakthrough technology is qualified by a breakthrough on one or more technological attributes such as an order of magnitude performance increase, a radically new capability, or/and new engineering and physical principles. Additional breakthroughs can be associated with a breakthrough technology, for example, the removal of a reverse salient in an existing system or reaching breakeven performance for a new system. If the technology also creates a new usage, value proposition, market, or business model, it would qualify as a radical innovation.

CASE STUDY: BREAKTHROUGH STARSHOT

We apply the previously developed framework to a gram-sized spacecraft for a mission to another star, which is currently under development by the Breakthrough Starshot program [START_REF] Lubin | A Roadmap to Interstellar Flight[END_REF]. We will first apply the breakthrough dimensionnovelty matrix to this technology and subsequently, briefly address the question of whether or not this is a potential breakthrough technology.

The data for this case study was collected from a conceptual feasibility study of the Initiative for Interstellar Studies (i4is) prior to the announcement of the Breakthrough Starshot program in March 2016. The lead author of this article participated in this study as the system architect. A team of 14 people has collaborated virtually for a week to analyze various concepts for sending a spacecraft with a mass of 23 grams to the Alpha Centauri star system. The results of the feasibility study [START_REF] Hein | The Andromeda Study: A Femto-Spacecraft Mission to Alpha Centauri[END_REF] were subsequently reviewed by members of the Breakthrough Starshot committee and informed the Breakthrough Starshot program. As data sources, published reports, internal documents, and personal accounts from team members were used.

The concept for the Breakthrough Starshot mission was proposed in [START_REF] Lubin | A Roadmap to Interstellar Flight[END_REF]. The spacecraft consists of a power subsystem (small-scale nuclear battery), communication subsystem (laser optical communication), camera payload, and further typical spacecraft subsystems. In addition, a thin, highly reflective surface is attached to the spacecraft, which is intended to reflect an incoming laser beam. This sail-like structure is called laser sail. By reflecting the laser beam, thrust is generated. The laser beam is emitted by a ground-based laser beaming infrastructure with a beam power of about a hundred gigawatts. The spacecraft is put into an orbit around Earth and then accelerated via the laser beam to velocities of 10-20% of the speed of light, reaching the Alpha Centauri star system within 50 years, in order to send back photos of potential exoplanets. Figure 2 shows a swarm of these spacecraft approaching the Alpha Centauri star system. [START_REF] Hein | The Andromeda Study: A Femto-Spacecraft Mission to Alpha Centauri[END_REF] For applying the breakthrough technology framework, we first need to define the system and component technologies. We treat the combined spacecraft and beaming infrastructure as the system.

ICED

The key component technologies are the fiber-optic lasers that form the phased laser array and the laser sail which consists of a highly reflective dielectric material. A phased laser array prototype for the beaming infrastructure has been tested in a laboratory environment [START_REF] Lubin | A Roadmap to Interstellar Flight[END_REF]. However, scaling these lasers up to hundred gigawatts of beaming power requires additional technologies such as the development of new types of beam guides for assuring the coherence of the beam. In addition, such high power densities have not yet been applied to reflective surfaces such as the laser sail. New, unknown physical effects could occur. Laser sail materials with the required reflectivity (99.999%) do exist. However, it is unlikely that the same substrate material (glass) can be used.

Is this system a potential breakthrough technology? It is clear that the underlying engineering and physical principles are new. But we also need to look at the potential performance, which is the velocity of the spacecraft. Reaching a nearby star within 50 years requires a thousand-fold increase in velocity compared to the fastest spacecraft that have left our Solar System. Both technological breakthrough criteria are satisfied on the system level as well as both potential breakthrough technology criteria. Hence, we are dealing with a potential breakthrough technology. Table 5 shows the resulting breakthrough dimension -novelty matrix for the Breakthrough Starshot system.

New usage

Operation of the beaming system and spacecraft swarm novel and knowledge to be developed

Value for stakeholders

Potentially interstellar exploration based on large spacecraft numbers: Value yet to be explored

New business model

Not yet defined Is this breakthrough enabled at the system or component level? Component technologies are combined, in order to deliver a new capability at the system level (reaching another star within a human lifespan). These component technologies exist at least as prototypes. Low-cost, high efficiency lasers are now available, due to an exponential decrease in cost and continuous increase in efficiency over the last decades, miniaturization is moving spacecraft from tons to kg-sized spacecraft to gramsized spacecraft, and novel, highly reflective, light-weight laser sail materials are under development [START_REF] Atwater | Materials challenges for the Starshot lightsail[END_REF]. Nevertheless, it seems that these technologies are rather a result of an accumulation of incremental improvements.

Table 6 shows the breakthrough dimensionnovelty matrix for the laser sail component technology. Some of the potential materials for the laser sail are based on new engineering and physical principles, such as meta-materials and nano-engineered materials [START_REF] Atwater | Materials challenges for the Starshot lightsail[END_REF]. These materials imply a considerable conceptual and knowledge expansion. Regarding performance, the conceptual expansion is rather minimal, as using laser sails for propulsion is a well-known concept. However, the knowledge of doing so at extremely high power densities requires a significant expansion of existing knowledge in how to engineer the sail at the nano, micro, and macro-scale.

ICED

Regarding usage, the proper operation of a laser sail under space conditions is still subject to numerous unknowns, starting from deployment and its behavior during the propulsion phase. The potential value for stakeholders is relatively clear (sail for in-space propulsion). However, the knowledge of how to exploit the sail for this purpose is still to be developed. A new business model has not been defined. To summarize, the laser sail seems to be rather based on an expansion of knowledge, rather than the introduction of a new concept. Only for some of the potential materials under consideration, it would qualify as a potential breakthrough technology. To conclude, combining component technologies that are not necessarily breakthrough technologies themselves, may lead to the creation of a potential breakthrough technology. An observation from this exercise is that it is important to carefully define the reference point for the analysis. Is Breakthrough Starshot compared to existing propulsion systems or is it compared to the prior art of laser sail propulsion concepts? Is the knowledge expansion assessed with respect to a specific organization or in general [START_REF] Garcia | A critical look at technological innovation typology and innovativeness terminology: a literature review[END_REF]?

Finally, the study focused on technological feasibility, using calculations based on physics principles for fundamental mission parameters and on financial feasibility, using high-level analogy cost calculations. The approach partly resembles the Exploratory Engineering approach proposed by [START_REF] Drexler | Radical Abundance[END_REF] but was supplemented by the engineering knowledge categories presented in [START_REF] Vincenti | Engineering knowledge, type of design, and level of hierarchy: further thoughts about what engineers know[END_REF], including typical engineering considerations such as using extrapolations from existing spacecraft components.

CONCLUSIONS

In this paper, we propose a conceptual framework for breakthrough technologies, in order to provide a basis for future engineering design methods, aimed at the development of products or systems using potential breakthrough technologies. A breakthrough technology is a technology that achieves a breakthrough, e.g. removing a reverse salient, achieving a 10 times performance increase, or introducing a radically new capability. We apply the framework to the case study of a laser-sail propelled interstellar probe, which is currently under development. The case study demonstrates, how the conceptual framework captures various subtleties that emerge during the assessment of a potential breakthrough technology. We conclude that the relationship between component and system-level breakthrough technologies requires further exploration. Furthermore, the coupling between the breakthrough technology and market breakthrough in the form of a new business model seems interesting for future work.

Figure 2 .

 2 Figure 2. Concept for a gram-sized interstellar probe[START_REF] Hein | The Andromeda Study: A Femto-Spacecraft Mission to Alpha Centauri[END_REF]

Table 1 :

 1 Comparison between breakthrough technology and major innovation categories from[START_REF] Garcia | A critical look at technological innovation typology and innovativeness terminology: a literature review[END_REF]

	Attribute		Breakthrough	Radical innovation	Really new	Incremental
			technology		innovation	innovation
	Major	technology	Always	Always	Sometimes	No
	discontinuity
	Major	market	Causes sometimes	Always	Sometimes	No
	discontinuity
	10 times performance	Always	Sometimes	Sometimes	No
	improvement or new
	capability

Table 2 :

 2 Novelty categories in terms of C-K expansion

	ΔC-δK: Conceptual innovation -New
	conceptual idea but minor knowledge
	expansion (Example: chair without legs)

Table 3 :

 3 Matrix with breakthrough dimensions as rows and degrees of C-K expansion as columns for the Wright Flyer in 1903

	ΔC-δK	δC-ΔK	ΔC-ΔK	δC-δK
	New engineering	Known airplane engineering
	/ physical	principles were significantly
	principles	expanded in terms of
		knowledge (aerodynamic
		coefficient, control, engine
		performance)
	New function /	Novel function (controlled,
	improved	crewed, heavier-than-air
	performance	flight) and performance
		(staying in the air for about
		a minute)
	New usage
	Value for	Not yet defined
	stakeholders
	New business
	model

Table 4 :

 4 Breakthrough dimensionnovelty matrix for the Wright 1909 Military Flyer

	ΔC-δK δC-ΔK	ΔC-ΔK	δC-δK
	New engineering /	Increase in reliability of initial
	physical principles	Wright Flyer and minor design
		changes
	New function /	Novel function and performance
	improved	for the military context without
	performance	sufficient prior knowledge of
		military needs
	New usage	Operations of military
		observation airplane
	Value for	Observation aircraft for the
	stakeholders	military
	New business model	Selling military airplanes with
		superior mobility over balloons

Table 5 :

 5 Breakthrough dimensionnovelty matrix for Breakthrough Starshot system

	ΔC-δK	δC-ΔK	ΔC-ΔK	δC-δK
	New engineering /		First fast laser sail propulsion system with still many
	physical principles		unknowns related to underlying engineering principles
	New function /		Potentially orders of magnitude higher probe velocities; large
	improved		functional knowledge expansion
	performance

Table 6 :

 6 Breakthrough dimensionnovelty matrix for Breakthrough Starshot: Laser sail

	ΔC-δK	δC-ΔK	ΔC-ΔK	δC-δK
	New engineering /	New material concepts with
	physical principles	different engineering and physical
		principles
	New function /	Existing sail function but different
	improved	functional knowledge
	performance
	New usage	Known usage in interstellar mission but
		significantly different operational
		parameters
	Value for	Known value for system developers but
	stakeholders	different knowledge required for
		exploiting value generated
	New business model	Not yet defined


domain: chim sde

text:
Natascha Schmidt

Vincent Fauvelle

Javier Castro-Jiménez
email: javier.castro-jimenez@mio.osupytheas.fr

Katixa Lajaunie-Salla

Christel Pinazo

Christophe Yohia

Richard Sempéré
email: richard.sempere@mio.osupytheas.fr

Occurrence of perfluoroalkyl substances in the Bay of Marseille (NW Mediterranean Sea) and the Rhône River

Keywords:

Four perfluoroalkyl substances (PFAS) were analyzed in 62 duplicate surface water samples from the Rhône River and Marseille Bay (France; NW Mediterranean Sea). Perfluorooctane sulfonate (PFOS) was detected in all samples and exceeded the European Environmental Quality Standard (EQS) values in over 80% of the cases. The most contaminated samples were from the Rhône River (up to 200 ng L -1 ∑ 4 PFAS), as well as those collected near a wastewater treatment plant outlet in Marseille Bay (up to 9 ng L -1 ∑ 4 PFAS). While PFOS was the predominant PFAS in Marseille Bay, remarkably high concentrations of perfluorohexanoic acid (PFHxA) were measured in the Rhône River (8-193 ng L -1 ). The relative abundances of individual compounds differed thus significantly between the Rhône River and Marseille Bay, indicating different sources. A simulation made with the MARS3D model showed that PFOS inputs from the Rhône River can enter Marseille Bay at levels > EQS.

Introduction

Perfluoroalkyl substances (PFAS) are a group of chemicals containing carbon-fluorine bonds, with varying perfluoroalkyl chain lengths. They show water and oil repellent properties and are used in a wide variety of application sectors: from textiles, inks and varnishes to firefighting foams (aqueous film forming foams, AFFFs) and for metal plating [START_REF] Paul | A First Global Production, Emission, And Environmental Inventory For Perfluorooctane Sulfonate[END_REF]. They are also used as additives in pesticides [START_REF] Sánchez-Avila | Spatial distribution and sources of perfluorochemicals in the NW Mediterranean coastal waters (Catalonia, Spain)[END_REF]. Perfluorooctane sulfonate (PFOS) is a widely used PFAS, which has been detected in freshwater and marine environments as well as in biota and humans [START_REF] Earnshaw | Comparing measured and modelled PFOS concentrations in a UK freshwater catchment and estimating emission rates[END_REF][START_REF] Kärrman | Identification and pattern of perfluorooctane sulfonate (PFOS) isomers in human serum and plasma[END_REF][START_REF] Naile | Perfluorinated compounds in water, sediment, soil and biota from estuarine and coastal areas of Korea[END_REF][START_REF] Sánchez-Avila | Spatial distribution and sources of perfluorochemicals in the NW Mediterranean coastal waters (Catalonia, Spain)[END_REF]. Historically, the US enterprise 3 M™ was the main producer of PFOS, but in 2000 the company declared to phase PFOS out. Since the demand for PFOS and PFOS-related compounds remained high, this phase-out led to a dramatic increase in the production of these chemicals in China [START_REF] Lim | Emission inventory for PFOS in China: review of past methodologies and suggestions[END_REF]. PFOS has been identified as a Persistent Organic Pollutant (POP) and was thus included in the Annex B of the Stockholm Convention in 2010, leading to restrictions in use and production. While PFOS in the environment can originate directly from industrial production and consumer goods, it can also be the result of degradation of its precursors. PFOS-precursors are usually substituted perfluorooctyl sulfonamides and a high variety of structures and degradation pathways exists [START_REF] Asher | Enantiospecific perfluorooctane sulfonate (PFOS) analysis reveals evidence for the source contribution of PFOS-precursors to the Lake Ontario foodweb[END_REF]. Perfluorooctanoic acid (PFOA) is another highly persistent PFAS under natural conditions. In addition to historical uses, PFOA can be generated from degradation of long-chain fluorotelomer precursor types and perfluorooctane amide related compounds [START_REF] Dasu | Aerobic soil biodegradation of 8:2 fluorotelomer stearate monoester[END_REF][START_REF] Mejia-Avendaño | Generation of perfluoroalkyl acids from aerobic biotransformation of quaternary ammonium polyfluoroalkyl surfactants[END_REF].

Growing evidence suggests toxicological effects of PFOS and PFOA on a variety of organisms [START_REF] Hagenaars | Toxicity evaluation of perfluorooctane sulfonate (PFOS) in the liver of common carp (Cyprinus carpio)[END_REF][START_REF] Xia | The use of spontaneous behavior, swimming performances and metabolic rate to evaluate toxicity of PFOS on topmouth gudgeon Pseudorasbora parva[END_REF][START_REF] Zhang | Evaluating the sub-lethal toxicity of PFOS and PFOA using rotifer Brachionus calyciflorus[END_REF]. For example, it is suggested that PFOS exposure (depending on exposure time and concentration levels) can lead to epigenetic changes in sea urchins and affect the cardiac development in fish [START_REF] Ding | Toxicity and DNA methylation changes induced by perfluorooctane sulfonate (PFOS) in sea urchin Glyptocidaris crenularis[END_REF][START_REF] Huang | Perfluorooctane sulfonate impairs the cardiac development of a marine medaka (Oryzias melastigma)[END_REF]. Annual average Environmental Quality Standards (EQS) have thus been derived for biota (9.1 μg kg -1 biota wet weight), freshwater (0.00065 μg L -1 ) and marine waters (0.00013 μg L -1 ) in the European Union (Directive 2013/39/EU).

The Bay of Marseille in the NW Mediterranean Sea is subject to different anthropogenic pressures including touristic activity on the coastline (especially during high season in summer) recreational and commercial activities in the Old Harbor ("Vieux Port"), as well as ferry, leisure and commercial harbors (e.g., at L'Estaque). Additionally, the local wastewater treatment plant rejects from 0.4 to 3.8 m 3 s -1 wastewater [START_REF] Oursel | Dynamics and fates of trace metals chronically input in a Mediterranean coastal zone impacted by a large urban area[END_REF] into the sea at its outlet (Cortiou) eastwards of the city in the Calanques National Park. At Cortiou, the small rivers Huveaune and Jarret (1-5 m 3 s -1 and 0.5-3 m 3 s -1 , respectively, [START_REF] Oursel | Dynamics and fates of trace metals chronically input in a Mediterranean coastal zone impacted by a large urban area[END_REF] also enter the Mediterranean Sea, except during strong rain events, when the river water is deviated. The Bay of Marseille, and more generally the Gulf of Lions, is also subject to high solar radiation [START_REF] Sempéré | Variability of solar radiation and CDOM in surface coastal waters of the northwestern Mediterranean Sea[END_REF] and strong wind regimes, which often make plant and plastic debris accumulate on the coast. Depending on wind forcing (among other factors), the Bay of Marseille can also be influenced by the Rhône River via freshwater intrusions [START_REF] Fraysse | Intrusion of Rhone River diluted water into the Bay of Marseille: generation processes and impacts on ecosystem functioning[END_REF][START_REF] Gatti | The Rhone river dilution zone present in the northeastern shelf of the Gulf of Lion in December 2003[END_REF][START_REF] Para | Fluorescence and absorption properties of chromophoric dissolved organic matter (CDOM) in coastal surface waters of the northwestern Mediterranean Sea, influence of the Rhône River[END_REF].

The Rhône River is the main freshwater source of the Mediterranean Sea since the damming of the Nile River and a major carbon source [START_REF] Sempéré | Carbon inputs of the Rhône River to the Mediterranean Sea: biogeochemical implications[END_REF]. It is 816 km long and has an average annual water discharge of 53 × 10 9 m 3 . The Rhône River has been strongly modified by human activities (e.g., dams, wastewater treatment plant inputs, hydro-electrical facilities) and has a history of polychlorinated biphenyls (PCB) contamination [START_REF] Mourier | Historical records, sources, and spatial trends of PCBs along the RhÔne River (France)[END_REF]. Recent studies also detected organic contaminants of emerging concern in its waters, such as phthalates and organophosphate esters [START_REF] Paluselli | Occurrence of phthalate acid esters (PAEs) in the northwestern Mediterranean Sea and the Rhone River[END_REF]Schmidt et al., submitted), along with micro-and macroplastics [START_REF] Castro-Jiménez | Macro-litter in surface waters from the Rhone River: plastic pollution and flows to the NW Mediterranean Sea[END_REF][START_REF] Schmidt | Occurrence of microplastics in surface waters of the Gulf of Lion (NW Mediterranean Sea)[END_REF]. Furthermore, various PFAS have been found in aquatic plants, benthic invertebrates and different fish species from the Rhône River [START_REF] Babut | Per-and poly-fluoroalkyl compounds in freshwater fish from the Rhône River: influence of fish size, diet, prey contamination and biotransformation[END_REF][START_REF] Miège | Occurrence of priority and emerging organic compounds in fishes from the Rhone River (France)[END_REF] showed that more than two-thirds of fishes analyzed had PFOS concentrations above the EQS.

The objectives of this study were: (1) to investigate the waterborne occurrence of PFOS and three other PFAS (perfluorohexanoic acid -PFHxA, perfluorohexane sulfonic acid -PFHxS and perfluorooctanoic acid -PFOA) in the Rhône River and Marseille Bay; (2) to perform a local risk assessment by comparing the measured concentrations with the annual average EQS values for water and; (3) to investigate the PFOS inputs into the Gulf of Lions and the Bay of Marseille associated to freshwater intrusion from the Rhône River by using a modelling approach.

Materials & methods

Study area and sampling

Surface water samples (1 L) were collected from April 2017 to April 2018 in duplicate in the Rhône River at Arles city (n = 2 × 13) and at three sampling stations in Marseille Bay: L'Estaque harbor (n = 2 × 6), Frioul island (n = 2 × 6) and WWTP-Cortiou (n = 2 × 6) (Fig. 1) using a stainless steel collector, poured into corresponding 1 L glass bottles and filtered (GF/F, 0.7 μm retention size; Whatman, Maidstone, UK) within 3 h after collection and either stored at 4 °C in the dark and extracted within 24 h or otherwise stored at -25 °C until sample processing. River water temperature was measured using a handheld electronic thermometer whereas river flow data were extracted from "Banque Hydro" (http://www.hydro.eaufrance.fr/). The river flow data used originates from a measuring station in Tarascon, about 16 km upstream of Arles. Since the Rhône River divides into two branches downstream of the flow-measuring station, but upstream of the water sampling station, it was considered that the river flow at the water sampling station corresponds to about 90% [START_REF] Sempéré | Carbon inputs of the Rhône River to the Mediterranean Sea: biogeochemical implications[END_REF] of the flow measured in Tarascon.

Chemicals and standards

Hexane, dichloromethane and acetone (used to pre-clean the SPE cartridges) were purchased from Promochem (Picograde, LGC standard) together with ethyl acetate. Methanol was provided by Biosolve (ULC-MS grade), whereas ultrapure water was obtained from a Millipore (resistivity > 18.2 MΩ) Milli-Q system. Native PFAS were obtained from AccuStandard (USA) and isotope labeled PFAS (internal standards) from Wellington Laboratories (Canada). SPE glass cartridges were prepared in the laboratory using 250 mg hydrophilic-lipophilic balance (HLB) Oasis ® (30 μm) bulk sorbent (Waters, Milford, USA).

Chemical analysis

Dissolved water phase samples were processed by solid phase extraction (SPE), using a method modified after [START_REF] Fauvelle | One-single extraction procedure for the simultaneous determination of a wide range of polar and nonpolar organic contaminants in seawater[END_REF] and analyzed for four PFAS (Fig. S1). Briefly, the filtrated water samples were vigorously shaken and passed through pre-cleaned glass cartridges using pre-cleaned polytetrafluoroethylene (PTFE) liners. Afterwards, 10 mL of ultrapure water were passed through the cartridges, which were then vacuum dried for 2 h. PFAS were eluted by using 5 mL of ethyl acetate followed by 5 mL of methanol. The extracts were then evaporated with pure N 2 gas until dryness and reconstituted using 990 μL methanol. Twenty ng sample -1 of PFHxA-13 C 5 and PFOS-13 C 8 were added as internal standards. PFAS were quantified using a LC-QTOF (Agilent 1290 Infinity LC system coupled with Agilent 6530 Accurate-Mass Q-TOF, Agilent Technologies, Les Ulis, France). Separation was achieved using an Agilent Zorbax Eclipse XDB reversed phase column (50 mm × 2.1 mm, 1.8 μm), with temperature set at 30 °C. Quantification was performed using the isotope dilution method, considering the native analyte to internal standard area ratio and solvent-based calibration curves. Instrumental details are available in the Supplementary material (Text S1, Table S2).

Dissolved organic carbon (DOC) was measured from filtered (GF/F, 0.7 μm), acidified (by 20 μL of 85% H 3 PO 4 acid) subsamples using a Shimadzu TOC-5000 carbon analyzer [START_REF] Sempéré | Distribution and bacterial availability of dissolved neutral sugars in the South East Pacific[END_REF]. The instrument blank (≤5 μM) was subtracted from all measured results. All organic contaminant and DOC analysis were conducted in duplicate. The GF/F filters used for particulate organic carbon (POC) and nitrogen (PON) analysis were acidified with 50 μL H 2 SO 4 (0.5 N) to remove inorganic carbon. POC and PON measurements were obtained using high combustion (1000 °C) on a CN Integra mass spectrometer (SERCON), calibrated using glycine references for every batch of 10-15 samples [START_REF] Raimbault | Distribution of inorganic and organic nutrients in the South Pacific Oceanevidence for long-term accumulation of organic matter in nitrogen-depleted waters[END_REF].

Quality assurance/quality control (QA/QC)

The whole procedure was conducted in an International Standards Organization (ISO) 6 cleanroom and strict QA/QC procedures were implemented. All glass materials and the GF/F filters were baked (450 °C, 6 h) prior to use. Given that PTFE might be a source of PFAS (at least at high temperatures; [START_REF] Schlummer | Emission of perfluoroalkyl carboxylic acids (PFCA) from heated surfaces made of polytetrafluoroethylene (PTFE) applied in food contact materials and consumer products[END_REF]), its use was limited to SPE sample loading lines and each PFTE line was cleaned thoroughly with MeOH prior to use in order to avoid sample contamination. Replicate blanks were made during each extraction and no contamination was detected in any of the blanks. Method recoveries obtained during a previous method validation ranged from 73 ± 14 (PFHxS) to 124 ± 5 (PFOA)% [START_REF] Fauvelle | One-single extraction procedure for the simultaneous determination of a wide range of polar and nonpolar organic contaminants in seawater[END_REF]. Method limits of quantification ranged from 0.10 (PFOS) to 8.00 (PFHxA) ng L -1 . Concerning the linearity performance of the quantitative method, the linearity range was 0.5-200 ng mL -1 for the calibration curve, the R 2 varied from 0.997 (PFHxS) to 0.999 (PFOS) and the slope RSD ranged from 2.3% (PFOS) to 5.1% (PFHxS). Samples were collected in duplicates and the concentrations of duplicates were averaged.

Hydrodynamic model (MARS3D)

The hydrodynamic model used to study the PFAS inputs from the Rhône River into the eastern Gulf of Lions was the three-dimensional MARS3D model (3D hydrodynamic Model for Applications at Regional Scale, IFREMER) as described in detail by [START_REF] Lazure | An external-internal mode coupling for a 3D hydrodynamical model for applications at regional scale (MARS)[END_REF]. The high resolution MARS3D-RHOMA configuration was applied and validated for the simulation of oceanic circulation [START_REF] Pairaud | Hydrology and circulation in a coastal area off Marseille: validation of a nested 3D model with observations[END_REF] and the biogeochemical processes of the Bay of Marseille by [START_REF] Fraysse | Development of a 3D coupled physical-biogeochemical model for the Marseille Coastal Area (NW Mediterranean Sea): what complexity is required in the coastal zone?[END_REF] and was then used to reproduce realistic, observed conditions [START_REF] Fraysse | Intrusion of Rhone River diluted water into the Bay of Marseille: generation processes and impacts on ecosystem functioning[END_REF][START_REF] Ross | Impact of an intrusion by the Northern Current on the biogeochemistry in the eastern Gulf of Lion, NW Mediterranean[END_REF]. The model domain covered an area of 100 km × 48 km between the mouth of the Rhône River and Cape Sicié (Fig. S2), with a horizontal resolution of 400 m and 30 sigma vertical levels. The model takes into account the forcing through the NW Mediterranean general circulation, on the basis of a nesting strategy with the large scale MARS3D-MENOR configuration (1.2 km resolution) [START_REF] Nicolle | Modelling for anchovy recruitment studies in the Gulf of Lions (Western Mediterranean Sea)[END_REF]. It is forced by the Rhône River discharge, and by atmospheric conditions of the year 2017, with a spatially homogenous wind reproducing the temporal evolution simulated at the SOLEMIO station in Marseille Bay (Fig. S2) thanks to the meteorological WRF-ARW model, which was described in detail by [START_REF] Klemp | Conservative split-explicit time integration methods for the compressible nonhydrostatic equations[END_REF]. The high resolution of the WRF-ARW configuration was applied for the atmospheric circulation and reproduced realistic conditions [START_REF] Yohia | Genèse du mistral par interaction barocline et advection du tourbillon potentiel[END_REF]. The model covers an area of 864 km by 1400 km with a resolution of 2 km and is forced by the GFS model (NCEP/NOAA).

The simulation was run for the year 2017 using inputs of PFAS concentrations measured in the Rhône River during field campaigns in between April 12th and December 12th (data from Table 1).

Results and discussion

Σ 4 PFAS concentrations and estimated flux to the Mediterranean Sea

Total PFAS concentrations were higher in the Rhône River (ranging from 13 to 200 ng L -1 ) than in Marseille Bay (0.11-9 ng L -1 ); the lowest concentration (0.11 ng L -1 ) being detected in the Bay of Marseille (L'Estaque and Frioul stations; Table 1). Although the highest Σ 4 PFAS concentration observed in Marseille Bay was 9 ng L -1 near the Marseille-Cortiou-WWTP outlet, the concentrations were lower than those detected in the Rhône River. This could indicate that riverine sources are generally more important than coastal sources, that relatively low amounts of PFAS enter the WWTP, that an important dilution effect occurs after the wastewater enters the sea, or that the applied treatments efficiently important quantities of PFAS from the wastewater before releasing it into the sea. While it is difficult to clearly name the source of the high PFAS concentrations detected in the Rhône River, one possible explanation could be the textile industry. PFAS are commonly used for technical and outdoor clothing, and the Rhône-Alpes region is leading the French textile industry with 712 companies and > 15,000 workers (UNITEX, http://medef-aura.fr/rhone-alpespremiere-region-textile-francaise.html).

To roughly estimate the flux of PFAS into the NW Mediterranean Sea, the measured concentrations of each sampling event were multiplied with the corresponding daily river discharge. The estimated daily dissolved water phase Σ 4 PFAS flux from the Rhône River into the Mediterranean Sea varies thus between 0.72 and 27 kg day -1 (Fig. 2). The high variability results hereby from the high variability in measured PFAS concentrations and the high temporal fluctuations of the river discharge (between 460 and 3960 m 3 s -1 on sampling events). While the river discharge had important temporal fluctuations, we counted six sampling events with a discharge < 1000 m 3 s -1 and seven sampling events with a discharge > 1000 m 3 s -1 (three of which were > 2000 m 3 s -1 ), indicating a relatively good equilibrium of samples taken in situations of low and high water discharge. Still, the calculated flux can only be considered as a limited, rough estimation, but it gives a first idea of PFAS inputs from the dissolved phase of the Rhône River to the Mediterranean Sea. For individual compounds we calculated fluxes of 4.13-18 kg month -1 (PFOS), 2.45-27 kg month -1 (PFOA; not taking into account the one sampling date when PFOA was not detected), 13-783 kg month -1 (PFHxA) and 1.59-10 kg month -1 (PFHxS) when considering one month as equal to 30 days.

Relative abundances of individual compounds

In the Rhône River, the predominant compound was PFHxA, with its relative abundance varying between 62 and 97%, while PFHxS was the least abundant compound with < 1-7%. PFOS made up for 2-19% of the sample composition in the Rhône River. Interestingly, [START_REF] Miège | Occurrence of priority and emerging organic compounds in fishes from the Rhone River (France)[END_REF] did not detect any PFHxA in their fish samples from the Rhône River (PFOS was most abundant in their samples), indicating that the relative abundances of PFAS in biota and water samples can be very different, possibly due to the different bioaccumulation potential of individual PFAS, in relation to their different perfluoroalkyl chain length [START_REF] Simmonet-Laprade | Investigation of the spatial variability of poly-and perfluoroalkyl substance trophic magnification in selected riverine ecosystems[END_REF]. In contrast, in Marseille Bay PFOS was generally dominating the PFAS composition with 16-54% (WWTP-Cortiou), 45-100% (L'Estaque harbor) and 52-100% (Frioul island). Furthermore, PFHxS had sometimes a relatively high relative abundance with 14-61% in WWTP-Cortiou and 0-48% in L'Estaque and Frioul stations. PFOA was never detected in Frioul, once in L'Estaque station (with 55% relative abundance) and twice in WWTP-Cortiou (27% and 45% relative abundance). In the Rhône River PFOA abundance varied between 0 and 20% (Fig. 2). These results clearly indicate net differences in the relative abundance of PFAS in waters from Marseille Bay and the Rhône River, suggesting different sources and/or environmental processes. Moreover, WWTP-Cortiou exhibits a different pattern than the other two marine stations, with higher Σ 4 PFAS concentrations and differing relative abundances (lower PFOS abundance; PFHxS abundance always > 0). This is probably due to specific WWTP related PFAS inputs at the WWTP outlet, but it also indicates that Σ 4 PFAS compound composition can be variable at a small spatial scale and that the WWTP outlet does not necessarily have an influence on PFAS occurrence and abundance in the inner Bay of Marseille, even though this needs further investigations.

In the riverine samples, PFHxA was found at concentrations of 8-193 ng L -1 (Table 1). Our maximum PFHxA concentration detected is about 20 times higher than the one observed in the Danube River by [START_REF] Loos | Analysis of emerging organic contaminants in water, fish and suspended particulate matter (SPM) in the Joint Danube Survey using solid-phase extraction followed by UHPLC-MS-MS and GC-MS analysis[END_REF] (max. 8.5 ng L -1 ) and more than two-fold the highest amount measured by [START_REF] Munoz | Spatial distribution and partitioning behavior of selected poly-and perfluoroalkyl substances in freshwater ecosystems: a French nationwide survey[END_REF] during a French nationwide survey comprising 333 freshwater samples (max. 86 ng L -1 ). However, in accordance with our results, [START_REF] Munoz | Spatial distribution and partitioning behavior of selected poly-and perfluoroalkyl substances in freshwater ecosystems: a French nationwide survey[END_REF] observed that PFHxA concentrations in the Rhône River were very variable and could reach higher relative abundances than in other watersheds. The authors suggested that the high PFHxA amounts could hereby originate from a fluorochemical plant producing polyvinylidene fluoride. This factory is located over 250 km upstream of our sampling station, but given the persistence of PFAS [START_REF] Kunacheva | The emergence of persistent organic pollutants in the environment: the occurrence and treatment of perfluorinated compounds[END_REF][START_REF] Stahl | Toxicology of perfluorinated compounds[END_REF] and the high mobility of short-chain perfluorocarboxylates [START_REF] Ateia | The overlooked short-and ultrashort-chain poly-and perfluorinated substances: a review[END_REF], it could still be a possible explanation for the high PFHxA concentrations measured in this study. In a Mediterranean wetland area, up to 18.7 ng L -1 of PFHxA have been detected [START_REF] Lorenzo | Occurrence, distribution and behavior of emerging persistent organic pollutants (POPs) in a Mediterranean wetland protected area[END_REF]. In Marseille Bay, PFHxA was only detected once (at a concentration < LOQ) at WWTP-Cortiou station, where some freshwater inputs occur via the rivers Huveaune and Jarret. We thus suggest that high PFHxA concentrations could possibly be considered as a tracer of a riverine signature. This is in accordance with previous observations in the Atlantic Ocean where PFHxA was only detected in samples closest to the Amazon River mouth [START_REF] Schmidt | The Amazon Rivera major source of organic plastic additives to the tropical North Atlantic?[END_REF].

PFOS occurrence, estimated flux and modelled inputs to Marseille Bay via freshwater intrusions

PFOS was detected in all seawater and freshwater samples. In the Bay of Marseille, PFOS and DOC concentrations were positively correlated (p-value < 0.001), as has been observed before in seawater of the North Sea [START_REF] Ahrens | Spatial distribution of polyfluoroalkyl compounds in seawater of the German Bight[END_REF]. In the Rhône River, PFOS concentrations seem mainly driven by the magnitude of river discharge (pvalue = 0.002). However, DOC and POC concentrations are well correlated with river discharge (see Table S1 for all DOC, POC, PON and river discharge data), PFOS is also correlated with DOC in the Rhône River (p-value = 0.007). Hereby, the correlation is negative (i.e., an increase in DOC entrains a decrease in PFOS concentrations), in contrast to the correlation observed between DOC and PFOS in seawater samples from Marseille Bay (Fig. 3). The negative correlation between PFOS and river flowrate might indicate that the PFOS sources in the Rhône River are rather constant and the PFOS amounts are more or less diluted depending on the river discharge. Another explanation could be that the increased amount of suspended particulate matter (such as POC) during high river discharge might enhance the sequestration of long-chain PFAS and thus reduce the dissolved PFOS concentration.

In this study, 84% of samples had PFOS concentrations higher than the respective annual average (AA) EQS (i.e., 0.65 ng L -1 for freshwater and 0.13 ng L -1 for marine waters). All samples from the Rhône River and Cortiou station showed concentrations ~3-7 or ~8-26 times higher than the corresponding AA EQS, respectively. At L'Estaque station, 67% of samples had exceeding PFOS concentrations, whereas this was the case for only 50% of samples from Frioul station (Table 1). The Maximum Allowable Concentration (MAC) EQS for PFOS (36,000 ng L -1 in freshwater and 7200 ng L -1 in marine waters) was never exceeded in our study. A recent study showed that some invertebrates (Oligochaetes and Dytiscidae) and fish samples from the Rhône River also exhibited PFOS concentrations exceeding the EQS (EQS biota of 9.1 μg kg -1 ), with up to 27 μg kg -1 detected [START_REF] Babut | Per-and poly-fluoroalkyl compounds in freshwater fish from the Rhône River: influence of fish size, diet, prey contamination and biotransformation[END_REF]. It thus seems as if the Rhône River food web could be affected by the environmental PFOS contamination and potentially negative impacts on human health through fish consumption should be investigated. The highest PFOS concentration measured in this study was on 22/06/2017 in the Rhône River (4.6 ng L -1 ), where 1.8 ng L -1 was the lowest concentration observed (on 05/01/2018). These values are comparable to those of the River Rhine upstream of Leverkusen in Germany (1.41-6.38 ng L -1 , Möller et al., 2010) and Swedish Rivers (0.04-6.90 ng L -1 , Nguyen et al., 2017) as well as those of three samples collected in the Rhône River in 2012 (1.5-4.9 ng L -1 , [START_REF] Munoz | Spatial distribution and partitioning behavior of selected poly-and perfluoroalkyl substances in freshwater ecosystems: a French nationwide survey[END_REF]. Significantly higher PFOS concentrations of 36.3-703.3 ng L -1 were measured in the Yangtze River Estuary in China [START_REF] Pan | Sediment-water distribution of perfluorooctane sulfonate (PFOS) in Yangtze River Estuary[END_REF].

Using the PFOS concentrations measured and the corresponding daily river discharge, a PFOS input from the Rhône River into the Mediterranean Sea of 138-616 (mean 338, median 330) g day -1 was estimated. For comparison, we made the same calculation using data from [START_REF] Lorenzo | Perfluoroalkyl substances in the Ebro and Guadalquivir river basins (Spain)[END_REF] and [START_REF] Loos | Analysis of perfluorooctanoate (PFOA) and other perfluorinated compounds (PFCs) in the River Po watershed in N-Italy[END_REF] (mean PFOS concentrations 2.2 ng L -1 and 5.55 ng L -1 , respectively) together with the average water discharges of the Ebro and Po Rivers (426 m 3 s -1 and 1540 m 3 s -1 , respectively) and obtained a daily PFOS input into the Mediterranean Sea of 81 g from the Ebro River and 738 g from the Po River. However, the comparison with the Po River has restrictions, since the authors did not filter their water samples prior to analysis, in contrast to this study and the one from [START_REF] Lorenzo | Perfluoroalkyl substances in the Ebro and Guadalquivir river basins (Spain)[END_REF]. The Ebro River is, by drainage basin, the third largest river flowing into the Mediterranean Sea, but its discharge is restrained due to high water demands [START_REF] Lorenzo | Perfluoroalkyl substances in the Ebro and Guadalquivir river basins (Spain)[END_REF][START_REF] Struglia | River discharge into the Mediterranean Sea: climatology and aspects of the observed variability[END_REF]. For comparison, the Nile River has an average discharge of approximately 1200 m 3 s -1 [START_REF] Struglia | River discharge into the Mediterranean Sea: climatology and aspects of the observed variability[END_REF], but its drainage basin is by far the largest of all the rivers draining into the Mediterranean Sea (2.988 × 10 6 km 2 , compared to 0.098 × 10 6 km 2 for the Rhône River) [START_REF] Montreuil | Rivers of the Mediterrenean Sea: water discharge and nutrient fluxes[END_REF]. To get a better idea concerning global riverine PFOS inputs into the Mediterranean Sea, it would thus be important to obtain measurement data from the Nile River, as well.

The numerical approach chosen to investigate the PFOS inputs from the Rhône River into the eastern part of the Gulf of Lions allowed us to examine whether the Bay of Marseille is influenced by these inputs or not. Hereby, the simulation started on 01/01/2017 and the contaminants were injected continually with concentrations punctually updated at the dates for which measurement data was available, and with an interpolation between two dates. The temporal series (Fig. S3) indicate that in the Bay of Marseille, the first PFAS inputs originating from the Rhône River were perceivable at the beginning of October 2017 in L'Estaque and Frioul stations and approximately one month later -at much lower concentrations -in WWTP-Cortiou, which is farther away from the source and is rather protected from currents through the neighboring cliffs. In the vicinity of the Rhône River mouth, the modelled PFOS concentrations were quite high (≥1 ng L -1 ); R² = 0.81 negative effects on the aquatic food web in and near the estuary can thus not be excluded and require further investigations. Furthermore, even in the northern part of the Bay of Marseille (e.g., in L'Estaque), the PFOS input from the Rhône River is sometimes enough to exceed the EQS value (EQS of 0.13 ng L -1 ; see black isoline in Fig. 4) in these marine waters (Fig. 4). The maximum value simulated at l'Estaque on November 16th occurred during south-south-easterly winds, associated with the anticyclonic Marseille eddy, which is necessary to advect the diluted Rhône River waters toward the northern part of the Bay [START_REF] Fraysse | Intrusion of Rhone River diluted water into the Bay of Marseille: generation processes and impacts on ecosystem functioning[END_REF]. In contrast the south-westerly winds that occurred for example on October 31st moved the panache eastwards without generating the eddy necessary to reach the Bay of Marseille. Maps of the barotropic currents for the four selected dates from Fig. 4 can be found in the Supplementary material (Fig. S4).

Conclusion

Highest PFAS concentrations were detected in the Rhône River, followed by WWTP-Cortiou and the two other marine sampling stations. Relative abundances of individual compounds between samples from the Rhône River and Marseille Bay were strongly different, probably indicating different PFAS sources. PFOS concentrations were exceeding the annual average EU EQS values in over 80% of samples. As shown by our results and comparison with literature, PFOS concentrations exceeding the EQS seems to be a frequent situation and should encourage decision makers to enforce stricter measures to avoid and reduce the contamination of water bodies. While at Cortiou station the local WWTP and/or riverine inputs through the Huveaune and Jarret rivers are the most likely PFOS sources, the model simulation indicated that in L'Estaque station the exceeding PFOS concentrations couldat least partlyresult from inputs from the Rhône River. Our data furthermore suggest that up to 27 kg of dissolved water phase Σ 4 PFAS could enter the Gulf of Lion area in the Mediterranean Sea each day through freshwater inputs from the Rhône River. This points to the Rhône River as a possible major source of PFAS to the Mediterranean Sea and a monitoring with higher spatial and temporal resolution is needed to validate our observations. Model results could be improved by considering heterogeneous atmospheric conditions to better represent upwelling and river intrusion events.

Declaration of competing interest

None.

NFig. 1 .

 1 Fig. 1. Google Earth map of the study area in the Gulf of Lions (northwestern Mediterranean Sea, see upper left corner). The position of the river flow measuring station in the commune of Tarascon is indicated as well as the trace of the Rhône River and the sampling station in Arles city. A zoom of the Bay of Marseille (lower right corner) indicates the three marine sampling stations including L'Estaque harbor, Frioul island and WWTP-Cortiou.

Table 1

 1 PFAS concentrations (in ng L -1 ) measured in surface waters of the Rhône River and Marseille Bay. Asterisks indicate that the measured PFOS concentration exceeded the fresh-and seawater EQSs of 0.65 ng L -1 (Rhône River) or 0.13 ng L -1 (Cortiou, L'Estaque and Frioul).

Fig. 2 .

 2 Fig. 2. Relative abundances (in %) of the four PFAS at each sampling date at the four sites. For the Rhône River, the black line indicates the estimated daily flux (in kg day -1 ) of Σ 4 PFAS into the Mediterranean Sea.

Fig. 3 .

 3 Fig. 3. Relationships between PFOS concentrations and DOC (Bay of Marseille, Rhône River) or river discharge (Rhône River).

Fig. 4 .

 4 Fig. 4. Simulated PFOS distribution (with concentrations in ng L -1 ) in the eastern part of the Gulf of Lions, including the Rhône River mouth and the Bay of Marseille. The black isoline indicates a PFOS concentration of 0.13 ng L -1 , the EQS for marine waters. Four dates were chosen to represent different directions and extensions of the river plume. The color bar is limited between 0 and 1 ng L -1 to better represent low concentrations (including the EQS value of 0.13 ng L -1 ); note that dark red values can also represent concentrations > 1 ng L -1 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Acknowledgements

The project leading to this publication has received funding from the Agence de l'eau Rhône Méditerranée Corse Blue-POLUT project and the JPI Oceans PLASTOX project. The project has also received funding from European FEDER Fund under project 1166-39417. Thanks also to Michel Fornier, Dorian Guillemain and Deny Malengros for their help during sampling and to Patrick Raimbault and the PACEM-MIO platform for POC and PON measurements.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.marpolbul.2019.110491.