Boyan Brodaric

Eric Boisvert

Laurence Chery

Peter Dahlhaus

Sylvain Grellet

Alexander Kmoch

François Létourneau

Jessica Lucido

Bruce Simons

Bernhard Wagner

Enabling global exchange of groundwater data: GroundWaterML2 (GWML2)

Keywords: General hydrogeology, Geographic information systems, GroundWaterML2, Groundwater data standards

GWML2 is an international standard for the online exchange of groundwater data that addresses the problem of data heterogeneity. This problem makes groundwater data hard to find and use because the data are diversely structured and fragmented into numerous data silos. Overcoming data heterogeneity requires a common data format; however, until the development of GWML2, an appropriate international standard has been lacking. GWML2 represents key hydrogeological entities such as aquifers and water wells, as well as related measurements and groundwater flows. It is developed and tested by an international consortium of groundwater data providers from North America, Europe, and Australasia, and facilitates many forms of data exchange, information representation, and the development of online web portals and tools.

Introduction

Opportunities have never been greater for sharing hydrogeological data across national and international borders, and across governmental, industry and academic sectors. These opportunities are driven primarily by a pressing need to better understand our natural environment at all scales, especially continental and global (e.g. [START_REF] Boyd | Critical questions for big data, information[END_REF][START_REF] Mayer-Schonberger | Big data: a revolution that will transform how we live, work and think[END_REF]. Major challenges include meeting the expanding demand for water resources associated with human consumption, food production and energy resources [START_REF] Gorelick | Global change and the groundwater management challenge[END_REF][START_REF] Scanlon | Groundwater depletion and sustainability of irrigation in the US High Plains and Central Valley[END_REF], the potential impact of unconventional energy exploitation (e.g. AWA 2012; [START_REF] Vidic | Impact of shale gas development on regional water quality[END_REF][START_REF] Vengosh | A critical review of the risks to water resources from unconventional shale gas development and hydraulic fracturing in the United States[END_REF], the predicted impacts of changing climate (e.g. [START_REF] Taylor | Ground water and climate change[END_REF], as well as other ecological and environmental impacts (e.g. [START_REF] Nevill | Groundwater-dependent ecosystems and the dangers of groundwater overdraft: a review and an Australian perspective[END_REF].

The growth of hydrogeological data is another significant driver, magnified by its much greater availability due to technological advances and governmental open data policies [START_REF] Zuiderwijk | Open data policies, their implementation and impact: a framework for comparison[END_REF]. However, collecting more data and increasing its availability is only part of the solution to the major challenges, as there are limitations in how to transform this data into improved understanding of hydrogeological science and water management (e.g. [START_REF] Loch | Role of hydrology and economics in water management policy under increasing uncertainty[END_REF]). These limitations are largely due to the distributed custodianship and heterogeneity of groundwater data, making it difficult for the end-user to discover, access and harmonize the data. Although there may be an impressive volume of global groundwater data available, few users have the capacity or desire to overcome these difficulties.

An additional part of the solution is making disparate data interoperable-that is, making the data usable in a seamless manner regardless of its original heterogeneity. Data interoperability typically requires the transformation of data into a common representation readily understood by both the data supplier and consumer (Brodaric et al. 2016). Often this representation takes the form of a data standard developed and maintained by key stakeholders, one that is typically used within two main technological environments: (1) within data networks that supply heterogeneous data to users, or (2) within workflow systems that chain together diverse software for modularized processing of data. While online groundwater workflow systems are somewhat nascent (e.g. [START_REF] Klug | A SMART groundwater portal: an OGC web services orchestration framework for hydrology to improve data access and visualisation in New Zealand[END_REF], web-based groundwater data networks have become more prevalent. Such networks consist of distributed data sources that are managed autonomously and that possess heterogeneous data structure and content. Government initiated examples of such groundwater data networks include the Canadian 'Groundwater Information Network' [START_REF] Boisvert | GroundWater markup language (GWML): enabling groundwater data interoperability in spatial data infrastructures[END_REF]Brodaric et al. 2016); the United States 'National Ground-Water Monitoring Network' [START_REF] Blodgett | Progress on water data integration and distribution: a summary of select U.S. Geological Survey data systems[END_REF]Brodaric et al. 2016); groundwater aspects of the French 'Water Information System' [START_REF] Bdlisa | Dictionnaire des données: référentiel hydrogéologique (version 2) [Data dictionary: hydrogeological reference (version 2)[END_REF][START_REF] Bdlisa | Dictionnaire des données: référentiel hydrogéologique (version 2) [Data dictionary: hydrogeological reference (version 2)[END_REF], the New Zealand SMART system [START_REF] Klug | A SMART groundwater portal: an OGC web services orchestration framework for hydrology to improve data access and visualisation in New Zealand[END_REF][START_REF] Kmoch | A spatial data infrastructure approach for the characterization of New Zealand's groundwater systems[END_REF]; and the Australian 'National Groundwater Information System' [START_REF] Bom | National Groundwater Information System[END_REF][START_REF] Carrara | Groundwater information at the Bureau: providing a national picture[END_REF]. Outside of government, the Australian 'Visualizing Victoria's Groundwater' portal [START_REF] Dahlhaus | Federating hydrogeological data to visualise Victoria's groundwater[END_REF][START_REF] Dahlhaus | Making the invisible visible: assessing the impact of federating groundwater data in Victoria, Australia[END_REF] is an interoperable data network developed by university researchers. It is noteworthy that the growth of such data networks is not limited to groundwater science, but echoes a larger trend in the sciences generally and in hydrology particularly [START_REF] Brodaric | Water data networks: foundations, technologies and systems, implementations and uses[END_REF].

A consequence of the rise of water data networks is a growing imperative for their connection, which recognizes the need to build networks of networks to supply data for large-area science problems (e.g. [START_REF] Nativi | The GEOSS solution for enabling data interoperability and integrative research[END_REF]. As this need becomes more evident, particularly across political boundaries, the absence of an international groundwater data representation becomes more acute. In this paper, this gap is addressed through the establishment of GroundWaterML2 (GWML2), a new global standard for groundwater data. GWML2 has been developed by a group of international groundwater data providers collaborating within the Groundwater Standards Working Group of the Open Geospatial Consortium (OGC). It comprises the groundwater component of the WaterML2 suite of hydrologic data standards and best practices (WaterML2 2017), and consists of data structures and encoding guidelines for groundwater data. GWML2 has been successfully implemented and tested by a variety of major groundwater data providers from North America, Europe, and Australasia, and it is expected to complement emerging data standards for both surface water and atmospheric water to facilitate data exchange for the complete water cycle.

This paper describes the motivation behind the development of GWML2, the development methods, the representation itself, its testing and evaluation, its relation to other standards and relevant work, and a summary including possible future directions. Overall, it is shown that GWML2 is an effective data transfer mechanism and a useful interoperability aid for groundwater data.

Usage scenarios for GWML2

Five usage scenarios motivate GWML2. These represent common and important data delivery situations, categorized as commercial, policy-oriented, environmental, scientific, or technological. They are selected to guide the design of GWML2 and to provide evaluation criteria, inasmuch as the data required by these scenarios should be representable in GWML2 and transmittable from major groundwater data sources to enable the scenarios to be carried out.

The commercial scenario involves finding water wells and springs within an area to enable estimation of the cost to complete a new water supply well-for example, a consultant or water well driller could use a web tool to explore the local geology and inspect wells located near the target area. By investigating the surficial sediment and rock materials, water level, yield and total depth at each well, the consultant could infer the distance and materials to the water table, as well as the expected yield, and the driller could estimate the cost and timeline for drilling. The public are also able to assess online water well records and make independent estimates. This not only aids evaluation of drilling potential, but consequently might also influence property purchases. Key entities in this scenario include water wells, related measurements such as water levels, as well as various hydrogeological units such as aquifers or confining beds.

The policy scenario involves reporting on the state of groundwater in specific administrative districts, motivated in large part by European requirements. Involved is the collection and evaluation of geological and hydrogeological characteristics, as well as the quantitative and qualitative monitoring of chemical and physical indicators. This aids the overall assessment of a management area, especially one that crosses political borders, and typically requires synchronization of information collected by multiple state water authorities. Key entities include management areas, related hydrogeological units, and monitored information.

The environmental scenario enables environmental managers, water managers, and legislators to assess threats to groundwater dependent ecosystems. The role of groundwater in sustaining environmental values is of growing importance globally, particularly in arid countries such as Australia. Key items include depth to water table, monitored information on groundwater chemistry and biology, and flow between groundwater and surface water.

The scientific scenario focuses on the delivery of data for use in groundwater flow modeling and soil-water balance modeling, as one among a myriad of possible scientific activities. Key entities for such modeling include the hydrogeological and geophysical properties of aquifers and related measurements, as well as characteristics of water wells, water bodies, and water use.

The technologic scenario determines compatibility with other hydrogeological data representations such as database schemas and exchange formats, via conversion to and from GWML2. This is particularly important to enable data interoperability (1) within a groundwater data network, by converting between local databases and GWML2, or (2) between different data networks, by converting between GWML2 and local data formats such as the European-wide INSPIRE (INSPIRE 2013a,b) or North American GWML1 [START_REF] Boisvert | GroundWater markup language (GWML): enabling groundwater data interoperability in spatial data infrastructures[END_REF]. Involved are all entities from the previous scenarios.

Methods for developing GWML2

GWML2 developers include hydrogeologists and information scientists from a cross-section of major governmental and academic groundwater data providers. The development of GWML2 follows five steps, as shown in Fig. 1, beginning with a needs assessment and concluding with a tested design published as an international standard.

Step 1 involves the establishment of prototypical usage situations, as described in section 'Usage scenarios for GWML2', which form the requirements and testing criteria for GWML2. In step 2, key terms are identified from the usage scenarios and authoritative definitions are attached to ensure a common conceptual foundation as well as to frame GWML's scope (GWML2 Vocabulary, 2017). Step 3 involves the development of a technical design [START_REF] Brodaric | OGC WaterML2: part 4-GroundWaterML2 (GWML2)[END_REF]) expressed as three related information models that culminate in a specification for encoding data in XML (Extensible Markup Language; W3C 2008). In step 4 example encodings are developed for each component of GWML2, and these are made permanently available online alongside the design specification (GWML2 XML Examples 2017; GWML2 XML Schema 2017).

Step 5 tests the encodings in implementations across North America, Europe and Australasia to ensure satisfaction of the usage scenarios, thereby providing proof of feasibility (see section 'Implementation and evaluation of GWML2').

Results: the GWML2 design

As sketched in Fig. 2, GWML2 can represent a wide variety of entities associated with hydrogeological units, subsurface bodies of water, and man-made artifacts such as wells. A novel aspect of its design is the refinement of a water container pattern (from Boisvert and Brodaric 2012), which conceptually distinguishes (1) a container such as a rock body or sand unit, (2) the spaces (voids) hosted by the container, and (3) the fluids occupying those spaces. These distinctions enable properties to be attributed to each of the containers, fluids, or voids individually, as well as to their relations. For example, an aquifer vulnerability estimate is a property of the unit or its part, the volume of a fluid is a property of the fluid body, and the volume occupied by voids such as fractures or pores, is a property of the voids. In contrast, porosity is a property of the relation between a container and its hosted voids, if understood as the proportion of void volume to total unit volume.

Types of hydrogeological units in GWML2 are aquifers, aquifer systems, confining beds, and groundwater basins. Such units are understood to be subsurface volumes of earth material that serve as containers for fluids. Their physical boundaries are demarcated by hydrogeological characteristics or, in the case of basins, by groundwater flow divides. As fluid containers, units variously host voids and are associated with a wide variety of properties such as porosity, transmissivity, storativity, hydraulic conductivity, yield and so on. GWML2 allows hydrogeological unit properties, and many others, to be further categorized by the data provider-for example, the porosity property can be additionally categorized as effective porosity, total porosity, or any other type of porosity, and the yield property can be similarly further categorized as safe yield, sustainable yield, aquifer yield, or any other relevant notion of yield. Importantly, these categorizations do not replace the standard GWML2 property, rather they serve as an optional and supplementary description for it. In addition to such augmented categorization, GWML2 also allows multiple occurrences of property values. This enables, for instance, not only both total and effective porosity to be specified for a hydrogeological unit, possibly as summary values for the unit as a whole, but it also permits the specification of multiple property values scattered throughout the unit to capture their spatial distribution, which is especially required by the scientific modeling usage scenario. This flexible mode of representing property values is due to re-use of the ISO/ OGC Observations and Measurements standard (O&M; Cox Figure 3 illustrates the use of the GeoSciML and O&M standards in a partial GWML2 encoding for a Canadian aquifer system, namely the Appalachian External Zone. Encoded are multiple material compositions from GeoSciML (i.e. gsml:composition), prefixed with Bgsml^, and with the BShale^instance fully open. Also shown are some key characteristics of the hydrogeological unit, prefixed by Bgwml2ŝ uch as recharge (i.e. gwml2:gwUnitRecharge), discharge (i.e. gwml2:gwUnitDischarge), and the fully o p e n h yd r a u l i c c o n d u c t i v i t y d e s c r i p t i o n (i . e . gwHydraulicConductivity). The value for this latter property is represented as a complex Observation, prefixed with Bom^, and includes supplemental categorization of the property as a statistical median via the assignment of the BHydraulic Conductivity -Median^qualifier (i.e. for om:observedProperty). Note the omission of several sections in Fig. 3 for reasons of space and readability, as indicated by B[…snip…]^.

Hydrogeological units in GWML2 can also be associated with water budgets, discharge and recharge estimates and their geographical zones, as well as management areas. Fluid bodies in GWML2 refer to the fluid contained in the voids of hydrogeological units, including their biologic, chemical and material constituents. Fluid bodies can also be subdivided into nested parts such as plumes, and can host various surfaces such as a water table, piezometric or potentiometric surface. These surfaces can in turn host divides-that is, lines projected onto the surface to denote the divergence of flow direction within the fluid body. Types of flow represented by GWML2 include those within containers, as well as between containers. Intra-container flow is exemplified by the movement of fluid within a unit, and inter-container flow is exemplified by recharge and discharge.

Man-made artifacts in GWML2 consist of water wells and monitoring sites, as well as related measurements and calculations recorded as single values or multi-valued time series. Water wells can be described geologically, via reference to their host hydrogeological units, as well as by well logs that describe the lithology of the different units or various measurements along the length of the borehole such as those from borehole geophysics logging. Water wells can, of course, also be described by various hydrogeological characteristics such as water level depth and yield, and by construction characteristics associated with casings, screens, and seals. GWML2 monitoring sites are places where sensing devices periodically measure significant hydrogeological properties such as water level, flow rate, water temperature, and chemical composition, or where samples can be taken. Such sites are closely related to other entities in GWML2, for example water wells or springs, which can host the devices or the entity being monitored or sampled.

GWML2 also provides a framework for representing a wide variety of aquifer tests, from which hydrogeological properties can be determined. This might involve pumping or injecting fluid at known rates, and then observing changes in the water table over time, or injecting a tracer at some location and following its progression at observation points. GWML2 representation of such tests then interrelates data about initial conditions, test parameters and procedures, as well as sampling sites and pertinent entities such as wells and the targeted hydrogeological unit, in addition to the measured and calculated values for various GWML2 properties. If perchance an exotic property is missing in GWML2, it can be added as a supplementary categorization to an observation description. In this way, a wide variety of aquifer tests can

GW_Recharge GW_Discharge

GW_Spring GW_Divide

GW_IntraFlow GW_InterFlow

Land surface

GW_Aquifer

GW_ConfiningBed

GW_BodySurface

GW_FlowSystem

GW_Well

Confining bed

Confined aquifer

Bedrock aquifer

GW_Discharge

Pumping well

Unconfined aquifer

GW_FlowSystem GW_FlowSystem

GW_AquiferSystem

GW_Basin

Wellfield GW_MonitoringSite

GW_ManagementArea

GW_FluidBody

GW_Aquifer

GW_Aquifer

Fig. 2 Main entities represented by GWML2, labeled with GW be represented (see Brodaric 2017, pp. 106-115). A full description of the entities represented by GWML2, as well as their technical design, can be found in the standards specification [START_REF] Brodaric | OGC WaterML2: part 4-GroundWaterML2 (GWML2)[END_REF].

Implementation and evaluation of GWML2

GWML2 is successfully implemented by nine major providers of groundwater data, with the implementations collectively delivering a wide variety of data from diverse systems. Each component of GWML2 is served online from at least one data source, and many components are served by several sources (Brodaric 2016), enabling GWML2 to meet the following criteria:

& Deployability: implementation with existing open standards and technologies was relatively uncomplicated across a broad range of data systems, and the design was shown to be compatible with diverse software environments.

& Completeness: GWML2 was shown to cover the wide variety of key data types available in the data sources with minimal information loss. Moreover, successful encoding of each GWML2 component demonstrated conformance with the intended design. & Usability: the information delivered by GWML2 satisfied the primary needs of the usage scenarios, as demonstrated by the successful delivery of all key entities from disparate databases. While efficiency was not measured quantitatively, in all cases the implementations returned results in times acceptable to human users, as indicated in ad-hoc reports.

Overall usability, including satisfaction of several usage scenarios, is further demonstrated by the consumption of GWML2 data by various web applications. Figure 4 illustrates satisfaction of the commercial scenario as GWML2 water well information is visualized from the Canadian (Fig. 4a) and US (Fig. 4b) groundwater data networks (Brodaric et al. 2016) via the Canadian web portal. This visualization also demonstrates satisfaction of an important aspect of the technological Fig. 3 Partial GWML2 encoding for an aquifer system and its median hydraulic conductivity. B[…snip…]^denotes sections deleted for reasons of readability and space scenario, namely the conversion of GWML1 to GWML2. Satisfaction of the environmental scenario is demonstrated in Fig. 5, which shows GWML2 groundwater chemistry in support of groundwater dependent ecosystems displayed in the Australian VVG (Visualizing Victoria's Groundwater) web portal, and originating from a data network of federal, state and academic groundwater data providers [START_REF] Dahlhaus | Making the invisible visible: assessing the impact of federating groundwater data in Victoria, Australia[END_REF]. Figure 6 illustrates development of a groundwater flow model in MODDFLOW using GWML2 input data from a management area in New Zealand. When considered in tandem with the 3D visualization of the management area and model in Fig. 7 [START_REF] Kmoch | A context-based groundwater data infrastructure[END_REF], it is apparent that the scientific and policy scenarios are satisfied, inasmuch as a flow model was successfully constructed from GWML2 data, and from this several hydrogeological characteristics were attributed to the management area. These uses of GWML2 also highlight a significant additional benefit, namely that it facilitates the development of sharable hydrogeological software that can be built over a single normative data format.

Related work on groundwater data representation

Although data representations in hydrology are numerous, those focusing on groundwater are less common and can be categorized as (1) database schemas, (2) ontologies, and (3) data exchange formats. Groundwater database schemas provide a structure for organizing and managing groundwater information in data repositories, either for restricted scope (e.g. [START_REF] Chesnaux | Building a geodatabase for mapping hydrogeological features and 3D modeling of groundwater systems: application to the Saguenay-Lac-St.-Jean region, Canada[END_REF][START_REF] Gogu | GIS-based hydrogeological databases and groundwater modelling[END_REF][START_REF] Steward | The synergistic powers of AEM and GIS geodatabase models in water resources studies[END_REF][START_REF] Wojda | HydroCube: an entity-relationship hydrogeological data model[END_REF][START_REF] Oulidi | HydrIS: an open source GIS decision support system for groundwater management (Morocco)[END_REF], or for broad use [START_REF]III.11 INSPIRE data specification area management/ restriction/regulation zones and reporting units[END_REF][START_REF] Nešetřil | Groundwater data management system[END_REF][START_REF] Strassberg | A geographic data model for representing ground water systems[END_REF]. Ontologies are formally arranged vocabularies used by data networks to help find and use distributed data, with a focus on hydrology in general (Atkinson and GWML2 clearly falls into this third category of data transfer format, but it is conceptually differentiated from representations in all categories by its adaptation of the water container pattern (from Boisvert and Brodaric 2012; see section 'Results: the GWML2 design'), which distinguishes containers (e.g. aquifers), water bodies, voids (e.g. pore spaces), and their properties and relations, enabling distinct description of each, and thus a more precise expression of the data.

Summary and future directions

GWML2 is as an international standard for exchanging a wide variety of groundwater data, to meet increasing demands for such data in many scientific and societal endeavors. Testing has shown that GWML2 can be used successfully to deliver Fig. 7 3D visualization of GWML2 data for New Zealand management area, including related water wells from Fig. 6 (from Kmoch 2017) Fig. 6 USGS MODFLOW single layer volumetric grid generated from GWML2 input data for the Horowhenua district management area, New Zealand. White cells denote the hydrogeologically active area, and blue cells denote sites for input observations from water wells (from Kmoch 2017). Cells are volumes with variable elevation and depth, possessing many hydrogeological properties from GWML2 such as hydraulic conductivity. The total area shown is approx. 12 km × 16 km, with distance in metres indicated along each axis groundwater information from significant data providers to meet key usage scenarios. In this process, GWML2 has already impacted the design of groundwater databases maintained by these providers, and is being incorporated into their operational data delivery mechanisms. It is further informing the nascent development of ontology-based knowledge structures for the hydrological domain [START_REF] Hahmann | Semantically refining the groundwater markup language (GWML2) with the help of a reference ontology[END_REF].

Next steps for GWML2 involve its possible submission to the World Meteorological Organization for endorsement as a global hydrological standard, in concert with its WaterML2 siblings, to complement its current standing as a global geospatial standard. Possible future technical directions include the development of additional GWML2 encodings in languages other than XML, as well as the enhancement of standard content. While GWML2 provides a rigorous standard structure for groundwater data, in many cases, the items that populate that structure, in the form of controlled vocabularies, are not constrained-for example, GWML2 captures porosity or yield values associated with an aquifer and provides a means for specifying the particular type of porosity or yield. It does not, however, enumerate a controlled vocabulary of acceptable types of porosity or yield, leaving it to the data provider to determine these. As a result, GWML2 documents from different data sources will be structurally identically, but much of the content is likely to be heterogeneous. In essence, GWML2 assures structural interoperability, but only partial semantic interoperability of content. Advancement of standard content vocabularies for GWML2 is a future challenge.

Other potential work involves a Blite^version, to lower the entry barrier to GWML2, as well as advancement of the scientific modeling usage scenario to further test the efficacy of GWML2 in supplying data to, and between, groundwater modeling tools. Augmentation of the technologic usage scenario is also a possibility, to determine alignment with important standards such as with the ArcHydro Groundwater standard database schema [START_REF] Strassberg | A geographic data model for representing ground water systems[END_REF], and with emerging surface water schemas such as HY_Features [START_REF] Atkinson | OGC HY_Features: a common hydrologic feature model[END_REF]. It is anticipated that these and other future directions for GWML2 will continue to be coordinated by the OGC Groundwater Standards Working Group in collaboration with related activities in industry, academia, and government, to promote GWML2 adoption and further the overall aim of enabling groundwater data exchange and interoperability.

Fig. 1

 1 Fig. 1 GWML2 development method

Fig. 4 a

 4 Fig.4a GWML2 water wells from the Canadian Groundwater Information Network (GIN), displayed in the GIN web portal(Brodaric et al. 2016). b GWML2 water wells from the US National Groundwater Monitoring Network (NGWMN), displayed in the GIN web portal(Brodaric et al. 2016)

Acknowledgements Many thanks to the editors as well as to the formal and informal reviewers for their very helpful guidance, which led to significant improvements in the paper. Included among them are J. Devlin, D. Blodgett, T. Ferre, C. Langevin, and C. Rivard. The Federation University of Australia acknowledges the support of several contributors in the development and testing of GWML2, most notably Andrew MacLeod. Funding Information Funding for CSIRO and Bureau of Meteorology work is provided by Water Information Research and Development Alliance (WIRADA), and funding for Federation University Australia work by the 'Centre for eResearch and Digital Innovation' and the 'Victorian Broadband Enabled Innovation Program'. Funding for BRGM work is provided by its joint IT Research Center 'INSIDE' dedicated to innovation in Water Information Systems with the French National Agency for Biodiversity (AFB). Funding for the SMART Aquifer Characterization (SAC) programme at GNS Science, New Zealand, and the Interfaculty Department for Geoinformatics (Z_GIS), University of Salzburg, is provided by the Ministry of Business, Innovation, and Employment (MBIE), New Zealand. Funding for Natural Resources Canada (NRCan) participants is provided by the NRCan Groundwater Geoscience Program. Funding for U.S. Geological Survey participants is provided by the USGS Groundwater and Streamflow Information Program.

Open Access This article is distributed under the terms of the Creative Comm ons Attribution 4.0 International License (http:// creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.


Arnaud Grivet Sébert
email: arnaud.grivet.sebert@cea.fr2018

Jean-Philippe Poli
email: jean-philippe.poli@cea.fr2018

Material Classification from Imprecise Chemical Composition : Probabilistic vs Possibilistic Approach

In this paper we propose a method of explainable material classification from imprecise chemical compositions. The problem of classification from imprecise data is addressed with a fuzzy decision tree whose terms are learned by a clustering algorithm. We deduce fuzzy rules from the tree, which will provide a justification of the result of the classification. Two opposed approaches are compared : the probabilistic approach and the possibilistic approach.

Introduction

Customs and ports security is a major issue in Europe. Indeed, many illegal or dangerous substances such as drugs, weapons, explosives pass through customs. Unfortunately, systematic container inspections are impossible in practice because of the cost and time that would be required. The volumes passing daily through the major European ports such as Rotterdam, Antwerp or Hamburg are indeed enormous: for example, 461.2 million tons of goods passed through the port of Rotterdam in 2016.

Our work is part of the C-BORD European project which aims at determining the content of containers using various technologies. One of these technologies uses tagged neutrons, which allows to obtain the chemical composition of a volume of the container. From this chemical composition, we want to determine the materials present in this volume of the container. In order to bring more credibility to the final software used by the customs officers, we will also provide a justification for this classification. Fuzzy rules allow to avoid the "black box" effect since customs officers have access to a real explanation of the classification made by the software, and close to natural language : "the container may contain drug (confidence degree : x) because the quantity of carbon is high, the quantity of nitrogen is low and the quantity of oxygen is medium" for instance.

The proportions are obtained by different treatments that are beyond our control. Thus, the input data are imprecise and are accompanied by a measure of this inaccuracy. Fuzzy logic thus seems appropriate for the exploitation of such data.

Given the time required and the authorizations needed to use a neutron generator, we will have a small learning data set, even if all classes of relevant materials will obviously be represented. The idea is therefore to use fuzzy decision trees [START_REF] Chang | Fuzzy decision tree algorithms[END_REF], which have been applied successfully on various classification problems [START_REF] Akiyama | Application of fuzzy decision tree to analyze the attitude of citizens for wellness city development[END_REF][START_REF] Olaru | A complete fuzzy decision tree technique[END_REF]. The scarcity of training data and the intrinsic inaccuracy due to the preprocessing preclude conventional statistical learning approaches such as neural networks, SVM, etc. which also do not provide an explanation to users.

In this article, we adapt to imprecise data the classic two-step workflow consisting in using clustering methods to create relevant terms from data and then in building a decision tree to get either a probabilistic or a possibilistic classifier. We propose a comparison of these two approaches, as some authors did for other applied problems [START_REF] Huizing | A comparison of a possibilistic and a probabilistic classifier in a multitarget tracking environment[END_REF], [START_REF] Nikolaidis | Comparison of probability and possibility for design against catastrophic failure under uncertainty[END_REF].

The paper is structured as follows: section 2 describes the context of the application that motivates this work. Then, section 3 describes the method to induce rules from imprecise data. Section 4 presents the results of the different experiments we conducted. Finally, section 5 draws the conclusions of this paper.

Application context 2.1 Neutron inspection for container digging

The H2020 project C-BORD (effective Container inspection at BORDer control points) aims at securing borders by exploiting different technologies: e-noses, X-rays, photo-fission and tagged neutrons. The goal is to detect dangerous (explosives, nuclear materials, ...) or illicit (drugs, contraband, ...) substances in containers.

In this paper, we focus on the use of tagged neutron and material classification. As shown in fig. 1, we use a device which produces a neutron beam to focus on a certain voxel (i.e. a volume) of the container. The neutrons interact with the nuclei of the atoms contained in the voxel, producing new particles that can be detected by the matrix sensors which are positioned on the side of the container. These particles are thus characteristic of the atoms encountered in the examined voxel. The processing of the raw data is not the topic of this article but we quickly describe the principle in fig. 2. After different pretreatments, a global spectrum is obtained. In comparison with the characteristic spectra of each of the studied atoms, this spectrum is decomposed into individual spectra by a Bayesian process which makes it possible to deduce the chemical composition of the voxel, expressed in percentages. This process is based on simulation and we can easily get the mean and the standard deviation for each proportion in order to characterize the inaccuracy of the reconstruction. Fig. 3 shows the result of these treatments for an exposure to ceramics, and in which the inaccuracy is represented by "box plots".

Previous work

We barely found some articles concerning the use of tagged neutrons to characterize materials. This can be explained by several difficulties.

First, data are scarce because few acquisition campaigns can be conducted. That also explains why few papers address the recognition of materials from their chemical composition. Then, the inaccuracy of the chemical composition makes the task difficult for conventional statistical models. Finally, a not insignificant difficulty is that the device is insensitive to hydrogen atoms, and thus some materials cannot be distinguished.

For these reasons, previous works proposed visual analytics methods to represent the content of the voxels. In [START_REF] Aupetit | Visual analytics to check marine containers in the eritr@c project[END_REF], the authors proposed a Voronoi diagram to highlight the proximity, in terms of chemical composition, of the current voxel with voxels previously inspected and whose content is known (see figure 4). Thus, it is not a question of recognizing the materials inside the container but of displaying visually close and known containers in order to deduce the contents.

This approach has the advantage of not requiring learning or parametrization since it relies on the manual selection of a neighborhood. In figure 4, we can also see two classical representations that have been used in conjunction with this method. These are projections of the current voxel onto two triangles:

the "materials triangle" indicates the proximity of the voxel with metals, ceramics and organic materials; the "alert triangle" presents the ratios between carbon, nitrogen and oxygen and is useful to recognize organic materials (even if the hydrogen is not detected).

The latter triangle helps to distinguish between drugs and explosives. The main drawback of the visual analytics approach is that the operator must be able to interpret the different representations himself.

In practice, the mastering of these representations, particularly the Voronoi graph, can be difficult for operators who are not familiar with these visualization techniques. As part of the C-BORD project, we want to go further and propose a list of materials, and an explanation of the decision. It is to overcome these different difficulties that we want to use a fuzzy expert system.

Fuzzy material classification

To solve the classification problem we build a fuzzy decision tree [START_REF] Chang | Fuzzy decision tree algorithms[END_REF] from which fuzzy rules are extracted to provide the end-user with a justification of the result. Each node of the tree is split into child nodes by an attribute, i.e. a chemical element. The child nodes correspond to fuzzy terms induced by a strong partition of the domain of the chemical ratios, namely [0, 100] since they are percentages. If no pruning is performed, the tree has a maximal depth equal to the number of chemical elements used as attributes for the classification. An example of a tree is shown in fig. 5. The imprecise inputs are modeled as either probability or possibility distributions. In the probabilistic case, the distributions are Gaussian distributions normalized so that their integral on the domain of the input data, namely [0, 100], equals 1. In the possibilistic case, we tested triangular and Gaussian distributions normalized so that their maximum value is 1.

Root Few C Medium amount of C A lot of C Few N Medium amount of N A lot of N Few N Medium amount of N A lot of N Few O Medium amount of O A lot of O Few O Medium amount of O A lot of O
We chose to learn fuzzy terms and to build the decision tree in two separate phases.

Fuzzy terms learning

Among the various methods we tested, the best methods to learn linguistic terms turned out to be clustering techniques. We describe hereafter the adaptations of two clustering algorithms.

Measures of dissimilarity

We modified these algorithms using a dissimilarity adapted to imprecise data. We consider the following dissimilarity for the probabilistic case :

d(x, y) = 1 - b a min(f x (t), f y (t))dt (1)
where f x and f y are the densities of the distributions representing the data x and y, a and b are the bounds of the definition domain of the data, 0 and 100 in our case. This dissimilarity is actually a distance for continuous probability distributions but we will not prove it here for reasons of space.

In the possibilistic case, the integral is replaced by the max. We tested several algorithms and decided to study more thoroughly kmedoids and affinity propagation because they gave better results than kmeans and DBSCAN in particular. K-means implies to compute the distance between a data input and a centroid, which is a single point randomly chosen and hence cannot be modeled as an imprecise datum. Unable to use the previously defined dissimilarity, we used asymmetric dissimilarities (in the probabilistic case for example, the integral of the distance between the centroid and the moving point of the imprecise distribution). This incompatibility between the imprecise inputs and the single-point centroids might explain the poorer results. Using DBSCAN, we often obtained a very small number of clusters because the data distribution is quite continuous along the domain [0, 100]. Since DBSCAN works by analyzing the neighborhood of each data point, the absence of clear gaps in the data distribution prevents DBSCAN from splitting the data set.

K-medoids

We adapted k-medoids algorithm [START_REF] Kaufman | Statistical data analysis based on the L 1 norm and related methods[END_REF] to cluster the imprecise data by substituting the traditional Euclidean distance by the dissimilarity defined above. This well-known algorithm takes the number n of clusters as a parameter. It randomly chooses n objects from the dataset to be the initial centers of the clusters and the other objects are assigned to the closest center. In each cluster, the object minimizing the sum of the distances to the other objects is set as the new center. Then the algorithm alternatively updates the sets belonging to each cluster and the centers until convergence. The output is the best result over several initial random configurations.

Affinity propagation

We also tested the affinity propagation algorithm [START_REF] Frey | Clustering by passing messages between data points[END_REF]. In this algorithm, every data point is a potential cluster exemplar. A distribution of similarity for each pair of points is given as an input. Another parameter, a real called preference, is used to control the number of clusters.

The data points send "messages" to each other. A data point i sends to a data point k the responsibility r(i, k) which represents how much i is likely to be in a cluster whose exemplar is k. k sends to i the availability a(i, k) which represents how much k is available for i to be in its cluster. The exemplars are the points i such that r(i, i) + a(i, i) > 0 and a data point is assigned to the closest exemplar according to the given similarity. The responsibilities depend on the similarity distribution. Besides, the responsibilities are function of the availabilities and conversely. The algorithm successively updates the responsibilities and availabilities until the clusters converge. We implemented this algorithm using the similarity associated with the dissimilarity defined in 1.

From clusters to membership functions

From each cluster we deduce a triangular fuzzy term whose top, of value 1, is set at the center of the cluster. The slopes are induced by the other terms' tops under the strong partition constraint. The extreme sets are slightly different : they are right-angled trapezoids whose flat part ends at the bound of the domain. We can see an example of a five-set partition in fig. 7. More complex term shapes (trapezoids, pentagons) reduce the performance and even the accuracy in some cases.

Probabilistic approach

To build the fuzzy decision tree, we also need to adapt to imprecise data the definition of the membership degrees to the linguistic terms. In [START_REF] Duch | Uncertainty of data, fuzzy membership functions, and multilayer perceptrons[END_REF] and [START_REF] Tsang | Decision trees for uncertain data[END_REF], the authors proposed integration techniques to deal with relations between uncertain data and crisp terms. We generalized these techniques to imprecise data and fuzzy terms. Given f the density of the probability distribution representing the imprecision associated with the proportion of an element e in an example x, and µ v (t) the membership degree of the value t to the fuzzy term v, the membership degree of the imprecise example x to the fuzzy term v is :

μv (x) = 100 0 f (t)µ v (t)dt ( 2
)
This definition is illustrated in fig. 8 where the imprecision distribution is dilated 10 times for a better visibility.

The membership degree of an imprecise input x to a node n is defined as the product of the membership degrees to the linguistic terms associated with the ascendants of n, including n : where, for all node n , v n is the linguistic term associated with n , and A(n) is the set of the ascendants of n, including n. By convention, the degree of any input to the root is equal to 1 1 . Using this definition, we can compute the fuzzy entropy, inspired from [START_REF] Peng | Soft discretization to enhance the continuous decision tree induction[END_REF], which is the criterion to select which attribute will be used to split a node. We consider the "fuzzy frequency" of a class c in a node n :

d n (x) = n ∈A(n) μv n (x) (3
f r c/n = x∈Tr∩c d n (x) x∈Tr d n (x)
where Tr is the training set. We also define the "membership frequency" of the examples to the node n :

f r n = x∈Tr d n (x) m∈S x∈Tr d m (x)
where S is the set of the sibling nodes of n, including n.

The fuzzy entropy, according to an element e, used at a node N whose set of children is noted Chil(N ), these nodes corresponding to each fuzzy term relative to e, is then defined as :

E(N ) = - n∈Chil(N ) f r n c∈C f r c/n × log 2 (f r c/n )
1 Any other non negative real d0 would lead to the same results since it would only multiply the membership degrees of all examples to all nodes by d0.

where C is the set of the classes of the problem.

Each node n of the tree is split in child nodes regarding the linguistic terms corresponding to the chemical element which minimizes the entropy, thus maximizing the entropy gain G(n) = E(N ) -E(n), N being the father of n. This node splitting is processed until one of the following stopping criteria is reached : All the attributes have been used splitting the ascendants of the current node.

The sum of the membership degrees to the current node is less than a threshold fixed in advance.

The entropy gain is less than another threshold fixed in advance.

Possibilistic approach

The definition 2 is replaced by : μv

(x) = max 0 t 100 (min(f (t), µ v (t))) (4)
where the possibilistic norms max and min are used. Fig. 9 illustrates this definition in the case of a Gaussian modeling of the input datum. Note that this definition coincides with the possibilistic similarity defined in 3.1.1, applied to a datum and a linguistic term.

The membership degree of an imprecise input x to a node n is defined as the minimum of the membership degrees to the linguistic terms associated with the ascendants of n, including n :

d n (x) = min N ∈A(n) μv N (x) (5)
where, for all node N , v N is the linguistic term associated with N , and A(n) is the set of the ascendants of n, including n. We replaced the entropy by another splitting criterion, the non-specificity, proposed in [START_REF] Higashi | Measures of uncertainty and information based on possibility distributions[END_REF]. We consider an ordered discrete possibility distribution

(π i ) 1 i m such that ∀i ∈ [|1, m -1|], π i π i+1 and π 1 = 1.
We also note π m+1 = 0. The measure of non-specificity, called U-uncertainty is defined as follows :

U (π) = m i=2 (π i -π i+1 )log 2 (i)
In our case, π is the possibility distribution of the classes in the current node : for every class c in C we note We then sort (π c/n ) c∈C in the decreasing order and compute the nonspecificity using the formula above.

π c/n = x∈Tr∩c d n (x) max c ∈C x∈Tr∩c d n (x)
The stopping criteria are the same as in the probabilistic framework, the entropy gain being replaced by the non-specificity gain NSG(n) = U (N ) -U (n), where N is the father of the node n.

To avoid the bias due to the varying number of linguistic terms of the attributes, we decided, inspiring from [START_REF] Jenhani | Decision trees as possibilistic classifiers[END_REF], to normalize the non-specificity gain by the SplitInfo(n) =n ∈Chil(n) f r n × log 2 (f r n ) which is actually the potential fuzzy entropy generated by splitting the node n, ignoring the classes of the samples.

Rule generation

While the tree is being built, the fuzzy frequencies f r c/l of every class c in every leaf l are computed and stored in memory. We then obtain, for each leaf, |C| rules -|C| being the number of classes of the problem -, weighted by the associated fuzzy frequency which corresponds to the "certainty factor", as defined in [START_REF] Bounhas | A possibilistic rule-based classifier[END_REF]. For instance, in fig. 5, the leaf on the extreme right will induce the rules "if there is a lot of carbon and a lot of nitrogen, then the object is in class c", for all c in C.

Recognition of input test data

As both training and test data are imprecise, for every new test sample x, we compute the membership degree of x to every leaf of the tree using the very same definition as in the training phase (3 or 5). Given a class c, this membership degree is then conjugated by the appropriate T-norm with the certainty factor of each rule whose consequent is c and the results are summed up using the weighted voting method [START_REF] Ishibuchi | Fuzzy sets and Systems[END_REF] to obtain the confidence degree of the proposition x ∈ c :

conf(x ∈ c) = l∈L T (f r c/l , d l (x))
where L is the set of the leaves of the tree and T is the probabilistic (resp. possibilistic) T-norm × (resp. min). We finally deduce the distribution of the classes for the input x normalizing the confidence degrees. In the probability case, we then have :

∀c ∈ C, p x (c) = conf(x ∈ c) c ∈C conf(x ∈ c ) (6)
and in the possibilitic case :

∀c ∈ C, π x (c) = conf(x ∈ c) max c ∈C conf(x ∈ c ) (7)
4 Experiments

Data simulation

We decided to test several methods on simulated data while waiting for real data. To do so, we refer to the molecular formulae of the different materials -the classes of the problem. For each material m and each element e, we deduce from the formula of m the stoichiometric percentage of e in m. This percentage p is used as a reference around which we randomly and in an uniform way pick a value v in the interval [p -p × DI 100 , p + p × DI 100 ]. The span of this interval is proportional to p and to a parameter DI we call "degree of imprecision", used to control the level of imprecision of the generated data. We then generate a random standard deviation σ via a normal distribution of mean p 2 × DI 100 and standard deviation p 4 × DI 100 . The tuple (v, σ) constitutes an imprecise datum.

We ran the experiments with data generated from the molecular formulae of seventeen explosives and nine drugs, with a degree of imprecision of 15. Since the real data will be few because of the financial and temporal costs of the experiments, we decided to use training data sets with only ten samples per class, on which we performed five-fold cross validation. We finally averaged the results on five data sets.

In the probabilistic approach, we represented our data as Gaussian distributions. In the possibilistic case, we tested our method with both triangular and Gaussian distributions ; the following results are obtained with Gaussian distributions, with which the performance turned out to be much better.

Fuzzy partitioning

One of the parameters that affect the most the accuracy of our classification method is the number of linguistic fuzzy terms used to define the partition of each chemical ratio domain.

Comparison of two clustering algorithms

We tested our method, using the adapted k-medoids algorithm, over all the combinations of numbers of fuzzy terms from 2 to 14 fuzzy terms, for the elements carbon (C), nitrogen (N) and oxygen (O). Since the other elements are far less discriminative for the classification of the materials we focus on, the number of fuzzy terms for these elements is set to 5 for the moment to run quicker tests. The best combination of numbers of fuzzy terms in the probabilistic framework is 14 for carbon, 14 for nitrogen and 13 for oxygen. In the possibilistic framework, it is respectively 5, 13 and 14 terms.

We then tested affinity propagation algorithm. In the probabilistic case, in the light of k-medoids test, we set the same preference to the clustering for the partitions of C, N and O ratios. It gave slightly worse results (88%) than the best obtained with k-medoids (90%). In the possibilistic case, we also obtained slightly worse results than k-medoids ones (79% against 81%).

We can conclude that k-medoids algorithm is preferable for this problem since it gives results at least as good as affinity propagation but the parameter to be optimized -the number of fuzzy terms -is discrete whereas affinity propagation preference is continuous.

To improve the robustness of our method, it would have been interesting to split the training set in two parts in order to learn the fuzzy terms from different data from the ones used to build the tree. But since we have very few data, we decided to learn both the fuzzy terms and the tree from the whole training set.

Probability vs possibility

Fig. 10 shows the dependence of the correct classification rate on the number of fuzzy terms for both probability and possibility approaches. Here, the results are averaged on five data sets. We can clearly see that the probability framework (in dark green) gives better results than the possibilistic one (in light blue). We merged the numbers of terms for N and O in one axis using a technique thoroughly described below, in the explanation of fig. 11.

To avoid bias due to the differences in the sizes of the trees, we ran the test setting the entropy and non-specificity gain thresholds so that the number of leaves of the trees are similar in the two approaches : the average number of leaves is close to 500 for a threshold of 0.1 in the probabilistic case, and 0.15 in the possibilistic case.

We can then conclude that the probabilistic approach is better than the possibilistic approach for our problem of material classification from imprecise chemical data. One reason might be that the possibilistic T-conorm, max, does not take into account the whole distribution which represents the input datum, and only considers a single value. On the contrary, the integral used in the probabilistic model grasps the sense of the whole distribution by computing the average of all the contributions. sufficient to guarantee the injectivity of the representation but we multiplied by 14 to let a gap between two consecutive surfaces for the sake of visibility. We can see that higher numbers of terms for N and O increase the accuracy but that a relatively low number of terms for C is enough to obtain good correct classification rates. The best combination turned out to be 5 terms for C, 14 for N and 12 for O. In the following, we will present further results for the probabilistic framework, with this optimal combination.

Results analysis

In the probabilistic approach, our treatment of the imprecision of the data does improve the accuracy compared to the same method without taking into account this imprecision, i.e. considering the data as discrete valuesthe means of the imprecision distributions. Fig. 12 represents the difference of correct classification rate with and without imprecision treatment. The gain of the imprecision treatment increases with the degree of imprecision of the data (see the definition in 4.1).

Fig. 13 is a confusion matrix which summarizes the results of the probabilistic method on the 26-class drug/explosive problem with the optimal combination of 14 fuzzy terms for carbon, 14 for nitrogen and 13 for oxygen. We can see that the algorithm classes quite correctly both the explosives (seventeen first classes from the top in ordinate) and the drugs (six last classes). The correct classification rate is 88.08%.

We also tested the method with the same parameters on a more complex problem with 38 classes of drugs, explosives and benign materials. The accuracy obtained is a bit lower : 79% of correct classification (see confusion matrix in fig. 14).

Conclusion

We presented a workflow for explainable material recognition from chemical compositions, based on linguistic variables learning and fuzzy decision tree induction. We implemented both probabilistic and possibilistic approaches. The probabilistic framework is actually an hybrid probabilistic/fuzzy approach since it takes a Gaussian probability distribution as an input and apply a fuzzy inference process to it. The comparison between the two approaches showed that the probabilistic one provides better results.

The method takes into account the imprecision of the data in both training and evaluation phases. In the probabilistic case, it outperforms the method without imprecision treatment and this gain increases with the degree of imprecision of the input data. We obtained correct classification rates up to 85%.

Several refinements may allow us to enhance our method's accuracy in further work. We might improve the linguistic terms learning using other dissimilarities, and taking the samples' labels into account. We shall also experiment more sophisticated aggregation methods than the mere addition of the results associated to each leaf. Some post-pruning techniques could be used along with the pre-pruning criteria to avoid trees with too many rules. Simpler rules, corresponding to the intern nodes of the tree, might also be useful in the classification.

We will soon be able to evaluate our method on real data sets with high imprecision. Data acquisition on pure elements, chemical products, drug and explosive simulants are being performed. This will be a first step since we will eventually have to address the problem of recognition of mixtures and materials into matrices, that are very frequent in real life container voxels.

Figure 1 : Neutron inspection principle 3 Figure 2 :

 132 Figure 1: Neutron inspection principle

Figure 3 :

 3 Figure 3: Chemical composition obtained from ceramics simulation

Figure 4 :

 4 Figure 4: Screenshots of the different visualizations introduced in [2]

Figure 5 :

 5 Figure 5: Fuzzy tree for material classification

Fig. 6 Figure 6 :

 66 Figure 6: Similarity between two imprecise data -probabilistic modeling

Figure 7 :

 7 Figure 7: Five learned fuzzy sets

Figure 8 :

 8 Figure 8: Membership degree of an imprecise datum to a linguistic termprobabilistic modeling

Figure 9 :

 9 Figure 9: Membership degree of an imprecise datum to a linguistic termpossibilistic modeling

Figure 10 :

 10 Figure 10: Correct classification rate against number of fuzzy terms for both approaches

Figure 11 :

 11 Figure 11: Correct classification rate against number of fuzzy terms -two views of the same graph

Figure 12 :

 12 Figure 12: Gain obtained when taking the imprecision of the data into account

Figure 13 :Figure 14 :

 1314 Figure 13: Confusion matrix for drugs and explosives

Acknowledgment

This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 653323. We warmly thank S. Moretto, C. Fontana, F. Pino, A. Sardet, C. Carasco, B. Pérot and V. Picaud for their contributions before our work, for their availability and their expertise.