Rea Peltola
email: rea.peltola@unicaen.fr

jussive from a discourse perspective 

Keywords: deontic modality, verb mood, permission, obligation, jussive

This paper examines the representation of semantic vagueness in discourse as well as the connection between deontic modal meaning and third person reference through the semantics and uses of the Finnish jussive mood. The data used in the analysis come from a collection of newspaper texts and a corpus of dialectal speech. Analyzing jussive forms that give rise to various modal readings, I argue that the two poles of the deontic axis, permission and obligation, are simultaneously present, albeit highlighted to different extents, in the interpretation of a jussive clause. This binary nature of the jussive semantics reveals itself to be a discursive resource: it allows the position of the speaker and other intentional agents to be taken into account in regard to the event that is potentially taking place, thus presenting more than one point of view in the situation. The jussive mood can therefore be regarded as contributing to the dialogical dimension of language.

Introduction 1.1 Objectives of the study

The aim of this paper is to investigate the simultaneous presence of the two modal poles, permission and obligation, in the uses of the Finnish jussive mood. In line with the comprehensive grammar of Finnish [START_REF] Hakulinen | Iso suomen kielioppi [Comprehensive Finnish Grammar[END_REF](Hakulinen et al. : § 1667)), the term jussive refers, in this study, to the third person singular and plural as well as to the so-called passive form of the imperative mood. 1 In other words, in Finnish, the jussive is not a mood with a full personal paradigm of its own (as in the closely related Estonian), but neither is it just a function of the imperative. It has a morphological marker (kOOn/t) that is different from the other personal forms of the imperative.

Imperatives in general can produce either a permissive (Go ahead, eat it!) or an obligative reading (Stop it right now!) depending on the interactional context and the other elements present in the directive clause. In the case of the Finnish jussive, the two readings can be activated simultaneously, although one or other of the modal extremes can be foregrounded. This type of semantic vagueness (van der Auwera and Plungian 1998: 100-104) has been observed in the modal verbs and verb constructions of a number of languages. In the present study of a verb mood, my aim is to account for the co-occurrence of the two modal meanings in discursive terms. In other words, through a microanalysis of the jussive clause and its context, I investigate the pragmatic function of semantic vagueness. I suggest that, from a discursive perspective, the jussive is characterized by a modal openness, that is to say it allows for more than one point of view on the situation to be taken into account. Due to the third person reference, the jussive lends itself well to this function. It inherently opens up another perspective on the event in addition to the one shared by the speech act participants.

The following example illustrates the semantic complexity of the Finnish jussive mood. This example is an extract from an interview where the speaker is telling a story about a boat accident caused by a storm as people were on their way to the church. The speaker's grandfather was leading a group of people who were meant to have returned home by boat after the service.

(1) meijjäv voar [oli] sanonu että olkoo siinä ve-vene. ja ei muuta ku tul'vat sittem maita myötem pois sielt. (SA, Mäntyharju)

'our grandfather [had] said that the boat had to / could stay there. and that's it they returned by land.'

Meijjäv voar

[oli] sanonu että ol-koo siinä vene POSS.1PL grandfather AUX.IPF.3SG say.PST.PTCP COMP be-JUSS there boat We can see that the two readings of the jussive form olkoo are simultaneously activated. This is made clear by the two different translations into English ('had to / could'). I will analyze this extract in more detail later. This paper is organized into five sections. In the remainder of this section, I present the data that was used in the study (Section 1.2) and give an overview of the verb moods in Finnish (Section 1.3). Section 2 outlines the theoretical framework of the study with a discussion of the different aspects of the modal meanings of permission and obligation. I will also take a closer look in this section at the semantic structure of the jussive. In Section 3, I analyze the uses of the Finnish jussive against this theoretical background and, in Section 4, I discuss the results of the analysis in view of the dialogical dimension of language. Section 5 presents the conclusion to the study.

Data

The data consisted of 231 occurrences of the jussive, gathered from both the Finnish Language Text Collection (henceforth FTC), which includes newspaper texts, and the Syntax Archives (SA), which is composed of dialect data. The number of occurrences per database is shown in Table 1. References for the databases can be found in Appendix 1.

Table 1. Jussive occurrences per database

Corpus

Jussive occurrences

Finnish Language Text Collection 145

Syntax Archives 86

Total 231

The sample of 145 jussive occurrences in the FTC was drawn from the results of a search in the following categories of the corpus: Aamulehti 1999, Demari 2000, Hämeen Sanomat 2000, Kaleva 1998-1999, Karjalainen 1999, Turun Sanomat 1999. 2 For the Syntax Archives, the search was carried out in all dialect groups. 3 The areal distribution of the jussive occurrences obtained as a result of the search was regular: 42 occurrences came from the Western group of dialects, 44 from the Eastern group.

The data varied in terms of time, mode of production and social and regional distribution.

The FTC newspaper texts presented standard written Finnish of the late 1990s, while the dialect corpus provided regional spoken variants of Finnish from the late 19 th to the early 20 th century.

Although contrasting the use of jussive in different varieties is not the focus of this paper, some comparative remarks on the two types of data are made during the analysis.

The examples presented in this paper are given with their English translations. In order to make the structure transparent to the reader, an interlinear morphemic gloss is given for each jussive construction examined and its immediate context (see [START_REF] Glossing | Department of Linguistics of the Max Planck Institute for Evolutionary Anthropology[END_REF].

The abbreviations used in the glosses are explained in Appendix 2.

The morphosyntax and semantics of Finnish verb moods

Mood is a morphological category of the verb expressing deontic, dynamic and epistemic modalities. The relationship between mood (grammatical category) and modality (notional category) is comparable to that of tense and time (see Thieroff 2010: 2). I will present the Finnish system of moods in this section before moving on to a discussion of the different types of modal meanings in Section 2.

Finnish verbs have four moods: indicative, potential, conditional and imperative. 4 The formally unmarked indicative, shown in (2), is usually described as expressing categorical affirmations, although it can appear in various types of modal contexts. Following Bybee et al.'s (1994) typological grammaticalization theory, it has been shown that the Finnish potential, marked by the affix -ne-, as in (3), and conditional, constructed with the affix -isi-, as in (4), have both developed from expressions of intention (see [START_REF] Forsberg | Suomen murteiden potentiaali: Muoto ja merkitys [The potential mood in Finnish dialects: Form and function[END_REF][START_REF] Kauppinen | Puhekuviot, tilanteen ja rakenteen liitto: Tutkimus kielen omaksumisesta ja suomen konditionaalista [Figures of speech, the union of situation and structure: Study of language acquisition and the Finnish conditional[END_REF]. In contemporary Finnish, these two moods code different types of epistemic possibility, although the conditional has also preserved its intentional uses (see [START_REF] Kauppinen | Puhekuviot, tilanteen ja rakenteen liitto: Tutkimus kielen omaksumisesta ja suomen konditionaalista [Figures of speech, the union of situation and structure: Study of language acquisition and the Finnish conditional[END_REF].

(

) istu-Ø-n sit-Ø-1SG 'I sit' (3) istu-ne-n sit-POT-1SG 'I probably sit' (4) istu-isi-n sit-COND-1SG 'I would sit' 2
The second person singular imperative form corresponds to the vowel stem of the verb, entailing a gemination on the subsequent word boundary (5), whereas the first and second person plurals include the affix -kAA-(6, 7).

( When it comes to the jussive in Finnish grammar, it is regarded as the third person and the passive form of the imperative. It should be noted that in the literature on other languages, the term is reported as being used for a number of purposes. For example, in Estonian, another Balto-Finnic language, the jussive is not included in the imperative paradigm but instead displays a full personal paradigm of its own [START_REF] Metslang | Mood in Estonian[END_REF]. 5 It is thus considered to be a mood that is autonomous from the imperative mood. In Sorbian (Scholze 2010: 384),

Albanian [START_REF] Breu | Mood in Albanian[END_REF], Bulgarian and Macedonian (Lindstedt 2010: 412), the term jussive refers to an analytic form that includes a specific auxiliary or particle. According to Lindstedt (2010: 412), the analytic jussive is a Slavic and Pan-Balkan item.

In some studies, the jussive is not considered a mood but rather a meaning, function or illocutionary act operated by certain imperative forms, in particular the third person imperatives (see Johanson 2009: 489;Lindstedt 2010: 412, 415;Squartini 2010: 239). In all cases, even though the grammatical status of the form varies, the third person reference seems to be typical of jussive semantics. The third person reference of the Finnish jussive will be discussed later in this paper. I will now move on to the morphosyntactic characteristics of this mood.

In standard Finnish, the jussive is marked by the affix -kO 6 and the personal endings -On and -Ot, which are usually considered to be coding the difference between singular and plural (8, 9). The passive form is constructed with TA marking (10). The jussive also presents a compound form (11), coding the perfective aspect.

(8) istu-ko-on sit-JUSS-SG 'let him/her sit' (9) istu-ko-ot sit-JUSS-PL 'let them buy'

(10) sano-tta-ko-on say-PASS-JUSS-SG 'let one/them/people say' ( 11) ol-ko-on sano-ttu AUX-JUSS-SG say-PST.PTCP 'let it be said' However, when examining the jussive forms in colloquial language, it becomes apparent that the difference between the singular and plural is not coded in the verb form since the personal endings -On and -Ot both appear with no regard to the number of the subject NP. In fact, the final element of the jussive form occurs frequently without any closing consonant (12).

The neutralization of the opposition between singular and plural in third person imperatives has also been identified in other languages, although it is not very common (see Birjulin and Xrakovskij 2001: 27) In ( 13) and ( 14), the indicative and jussive verbs take an overt nominative subject (Pauli) and a genitive total object (kirjan). In (15), however, the second person imperative verb is in the clause-initial position, without a subject and followed by a nominative total object. 7 2. The semantics of the jussive 2.1 The two modal poles 2.1.1 Typology of modalities Linguistic modalities can be organized according to a dichotomy between necessity and possibility. On an epistemic level, factual events are necessarily true, counterfactual events necessarily false and nonfactual events possibly true or false (see, for example, Lyons 1977: 787). When it comes to non-epistemic modalities, the possibility end of the axis is represented by expressions of permission (deontic modality) or capacity and ability (dynamic modality), while the necessity pole corresponds to deontic obligation, such as speaker's intention and social norms, or dynamic constraints that are either internal to a person (different type of needs) or caused by the circumstances (see, for example, Palmer 2001, although he makes a slightly different distinction between deontic and dynamic modalities; [START_REF] Hakulinen | Iso suomen kielioppi [Comprehensive Finnish Grammar[END_REF]Hakulinen et al. : § 1554Hakulinen et al. -1557)). 7 In addition to the moods presented here, there is a form of the second person singular called optative with a very limited, archaic use, for example, tull-os ('come-OPT.2SG'). According to Lehtinen (2007: 130), this form was originally marked with the affix *γO, the weak grade of kO undergoing consonant gradation (for a discussion of the presence of this form in Finnish grammars, in Old Finnish and in the dialects, see Leskinen 1970: 19-37, 38-39, 66-75). According to a theory on the evolution of the Estonian jussive, the optative would have given rise to the gu-/ku-formed jussive of modern Estonian (Metslang and Sepper 2010: 546). This typology of modalities presupposes that the factors making a state of affairs possible or necessary are either participant-internal (capacity, need, intention) or participant-external (permission or norms coming from an authority, circumstantial constraints). On the basis of this division and using the typological grammaticalization paths of [START_REF] Bybee | The evolution of grammar: Tense, aspect, and modality in the languages of the world[END_REF] as a starting point, van der Auwera and Plungian (1998) developed the semantic map of modalities, taking into account both the diachronic and synchronic dimensions of the modalities. The typology also assumes that the different types of modalities imply different psychosocial and physical force oppositions, meaning the subject has a tendency toward an action and faces an external pressure of some kind opposing this tendency (see Talmy 1988: 77-88).

In what follows, I demonstrate that the Finnish jussive essentially codes both participantinternal and participant-external deontic modal meanings plus, more marginally, dynamic constraints. Instead of different propositional truth values (see, for example, Boye 2012: 31), the Finnish jussive brings to the fore intentional, personal agents as well as their position in regard to other agents and the circumstances.

Permission, obligation and agency

Deontic modalities involve the distinction between performative and descriptive expressions (see Nuyts 2005: 15), depending on whether the speaker is performing a linguistic act in order to influence the state of another participant or the circumstances or merely reporting the events.

In this paper, the concepts of permission and obligation are used in both senses. The two poles entail different types of speaker attitudes toward an event.

In the case of permission, these depend on whether the speaker actively authorizes an event initiated by another intentional agent to take place, thus making it possible, or whether the speaker acts passively in not opposing an event that takes place. In terms of force dynamics, the permissive relation can be regarded as a situation involving opposite forces, asymmetrical in their relative strengths, where the intrinsic tendency of one overrides the other (Talmy 1988: 77-88, see also Leino 2012: 223-227). Egan (2012: 69-70) illustrates the permissive meaning by a situation in which the permitter enables the permittee to pass, on a conceptual level, either by removing a barrier blocking the path of the latter or by not imposing any barrier. In the case of barrier removal, the prior existence of a barrier is inferred on the basis of the immediate co-text or on our general knowledge of the world. For example, when interpreting the clause Claudia relaxed her fingers, letting the pencil drop to the desk, we use our knowledge of the physical world and conceive the fingers as the barrier removed (Egan 2012: 71-72).

Obligation can also involve either a direct speech causation, in other words a directive function, or a description of a necessity imposed on one of the participants. In both cases, the intention of the participant figuring as the source of the necessity is foregrounded, whereas the meaning of permission is based on the pre-existence of another agent's will or other form of necessity toward which the subject directs their (permissive) attitude (see, e.g., [START_REF] Fortuin | From necessity to possibility: The modal spectrum of the dativeinfinitive construction in Russian[END_REF]: 55, Hans-Bianchi 2012: 129). The difference between permission and obligation can thus be accounted for in terms of different perspectives on the event.

Apart from events that are (potentially) instigated by another intentional agent, the permissive relation can involve an event that is otherwise independent of the subject's will, for example, a self-induced motion of an entity or a natural course of events (see, e.g., von Waldenfels 2012: 210-213). This was the case in the example above, Claudia relaxed her fingers, letting the pencil drop to the desk, where the pencil is not conceived as an intentional being but merely as an entity subject to gravity.

The various deontic readings are thus based on the presence or absence of other intentional participants in the event. In the case of an expression of deontic necessity, the speaker instigating the obligation is obviously viewed as being in control of the event. However, the speaker permitting is also inherently an agent with will because even the act of not opposing is a choice, which implies the capacity, at least theoretically, to control the situation (see Laitinen 1992: 176-177;Leino 2012: 236). 8 Like obligation, permissive meaning can only occur in a situation where the agent has control over the state of affairs (see, however, the discussion on the permeability of the border between controllable and uncontrollable actions in Birjulin and Xrakovskij 2001: 17-18).9

Permission, obligation and time

There is one more aspect of permission and obligation that should be pointed out before moving on to an analysis of the jussive occurrences. The relationship of permissive meaning to time is different from that of obligation. Consider the following semantic definition of imperative sentences:

Imperative sentences are positive or negative sentences conveying the idea of direct speech causation that can be interpreted as: "The speaker [=prescriptor], wishing (or not wishing) action P (which is either being or not being performed at the moment of speech) to take place, informs the listener [=recipient of prescription] as to who should (or should not) be the agent of action P [=performer of the prescribed action], thus attempting to cause (or prevent) action P by the very fact of this information". According to this definition, the aim of any imperative sentence in general consists in either changing the existing reality (i.e. transforming a certain imagined world into a real one) or preserving it. (Birjulin and Xrakovskij 2001: 5) With an imperative clause coding obligation, the speaker aims to cause action P. Since action P has not yet taken place, these imperative clauses entail a future reading, which is not inherent in the same manner to permission clauses. Expressions of permission that code the absence of speaker opposition (not imposing a barrier) and which are therefore not regarded as active authorizations ("making something possible") can refer to events that have already taken place. They do not involve a change but rather the continuation of an already existing state of affairs (on the different combinations of directivity and the concepts of change and continuation, see Birjulin and Xrakovskij 2001: 11-13). Consider the following example, extracted from the newspaper corpus, concerning the opinion of a German newspaper on the Finnish municipality Urjala:

(16) Olkoon vaan Urjala saksalaislehden mukaan persläpi, mutta nuoret tahtovat asua siellä.

(FTC, Aamulehti 1999.)

'Urjala may be a real hole, according to the German newspaper, but young people want to live there.'

Ol-koon vaan Urjala saksalais-lehde-n mukaan pers-läpi, be-JUSS PTCL PROP german-newspaper-GEN according.to ass-hole mutta nuore-t tahto-vat asua sie-llä. but young-PL want-3PL live PROADV-ADE

In this concessive clause, the speaker admits the negative description given by the German newspaper of the Finnish municipality. The event of admitting is posterior to the event of describing. The permission that gives rise to the concessive reading is thus addressed toward a state of affairs that has already taken place.

The permissive meaning as such does not foreground the temporal connections and truth value of the proposition but, rather, the position of the speaker and of another intentional agent in regard to it. This is due to the difference in scope between modalities. Epistemic modalities have a wide scope, operating over the whole proposition, whereas dynamic and deontic modalities focus on parts of the proposition, particularly on the agent of the action (the interlocutor or someone else) (see, e.g., Radden and Dirven 2007: 238).

Unlike the indicative and conditional moods, the jussive (along with other forms of the imperative paradigm and the potential mood) does not inherently involve temporal structuring, which would determine the relationship between the moment of event and the moment of speech (see Peltola 2011: 129-214). In this sense, the Finnish jussive can be counted among the verb forms that leave the temporal and epistemic interpretation of the event undetermined, to be defined by contextual factors (for a similar analysis of the French subjunctive, see Gosselin 2005: 94-96, 186).

Modal openness

As with the first and second person imperative forms, the jussive is an element allowing the speaker to express his will concerning the action or state of another participant or the state of circumstances (see [START_REF] Birjulin | Imperative sentences: Theoretical problems[END_REF] semantic definition of imperative clauses above). In the analysis of the data presented below, we will see that this intentionality gives rise to a number of modal readings depending on the contextual factors, such as the semantics of the verb, the presence or absence of an intentional agent (other than the speaker) and our general knowledge of the world.

As mentioned in the introduction, it is common for imperative forms to be used for expressing both commands and permission, depending on whether or not the denoted action is viewed as initially wanted by the agent. This is also true for the Finnish second person imperative. Example (17) contains a command, meaning the speaker wishes the interlocutor to act according to his will. Example (18) illustrates permission as the speaker displays adjustment to the will of another agent (here, the interlocutor).

(17) Ota tämä kirja.

En jaksa kantaa kaikkia yksin. take.IMP.2SG DEM.NOM book.NOM 'Take this book. I can't carry them all by myself.' (18) -Saanko ottaa tämän kirjan?

'Can I take this book?' -Ota vaan. 10 take.IMP.2SG PTCL 'Go ahead, take it.'

The relationship between the two modal meanings of ota ('take.IMP.2SG') in these examples is characterized by a certain degree of ambiguity, following the definition given by Tuggy (1993: 280-282). They share the same morphophonological form, but they are separable in the sense that it would be difficult to treat (17) as permission and (18) as a command.

When it comes to the modal meaning of the Finnish jussive, I argue that, rather than ambiguity, it is better described as semantic vagueness, or unspecificity. It is not about expressing different modal meanings in different contexts with the same form, as in ( 17) and ( 18), but about the simultaneous presence of both necessity and possibility, in other words the opposite modal meanings are inherently intertwined in the jussive semantic structure. This inseparability of the two (or more) meanings is typical of vague structures (see Geeraerts 1993: 228;Tuggy 1993: 275; for the difference between vagueness and polysemy, see also [START_REF] Haspelmath | The geometry of grammatical meaning: Semantic maps and crosslinguistic comparison[END_REF]. Another argument for the vagueness analysis is that in the case of negation, both modal readings are negated ('not p1 and not p2') (see Geeraerts 1993: 234, 248 It is not unfeasible that the same type of vagueness can also be found behind certain second person imperative uses. Forsberg's (forthcoming) analysis of the different degrees of directivity in uses of the Finnish imperative shows that the second person imperative also displays many non-directive uses, for example, that of disapproval.

The jussive is nevertheless worth examining separately because the third person reference makes it fundamentally different from the second person imperative. The jussive can be used either to refer to someone or something outside of the speech situation or to address someone present in the speech situation without introducing the polarity between the first and second 10 The presence of the discourse particle vaan is not a condition for the permissive meaning to occur, but the particle makes the meaning more explicit in this example (see Hakulinen et al. 2004: § 828).

11 For a discussion of the relationship between permission and obligation in negative contexts, see Fortuin (2005: 55-56). For a discussion of the conceptualization of negative permission, see Egan (2012: 81-82, 100-101).

person (for a discussion of the presence or absence of the third person referent, see Yamamoto In this example, the jussive clause allows the interlocutors to view the situation from more than one point of view, namely from that of the addressee of the invitation as well as from that of the two other participants. This is due to the third person reference (which places the polarity between first and second person to the background) and the semantics of the jussive where two modal meanings meet. The jussive is thus a form that leaves the referential and modal reading open to a certain extent. Figuratively, it can be regarded as a prism that splits the perspective from which the event is observed into more than one parallel point of view.

Modal vagueness, where the meanings of possibility and necessity co-occur, has been observed in a number of modal verbs and modal verb constructions in different languages. The Swedish modal verb få ('get') and its equivalent in Finnish saada display the same type of openness between permission and command reading as the Finnish jussive (see Viberg 2012):

(22) Swedish: Maria får gå hem. Finnish: Maria saa mennä kotiin.

'Maria is allowed to / has to go home.' [START_REF] Viberg | Language-specific meanings in contrast: A corpus-based contrastive study of Swedish få 'get[END_REF] for an exhaustive analysis of the semantics of saama, see [START_REF] Tragel | Grammaticalization of Estonian saama 'to get[END_REF].

Furthermore, it is not uncommon for the modal reading of the verb saama to be left open [START_REF] Tragel | Grammaticalization of Estonian saama 'to get[END_REF]Habicht 2012: 1394).

In the present study, the focus is on a verb mood. The analysis of the data presented below shows how semantic vagueness is represented in discourse and what the raison d'etre of this vagueness is in terms of interaction. I argue that, in the case of the Finnish jussive, even though the context may highlight one of the deontic modal poles, the other is nevertheless also present.

This simultaneous presence appears in discourse as modal openness, allowing more than one point of view on the event to be taken into account.

Necessity and possibility intertwined

In this section, I analyze the uses of the Finnish jussive, drawing attention to the coexistence of two modal readings, permissive and obligative, as well as to the dynamism between them. I begin by examining command and optative clauses, where the necessive meaning appears to be dominant (Section 3.1). My aim is to show that, in these clauses, along with the modal meaning displaying the speaker as an initiator of the action or at least as the source of the intention, there is another point of view on the event that is construed: that of a participant allowing the event to take place. In Section 3.2, the situation is reversed. I argue that the jussive clauses used for authorizing and consenting occur in contexts of decision-making. They thus function simultaneously as expressions of norm setting. In Section 3.3, I discuss a third group: jussive clauses that display obligation caused by circumstances. Finally, I present examples of grammaticalized and lexicalized jussive clauses in Section 3.4.

Necessity highlighted: Commands and optatives

When contextual factors do not present any reason to consider the event as initiated or wanted by another intentional agent, the jussive clause is interpreted as a command from the speaker to be followed by either the other participants of the speech situation or someone else. The use of the jussive in legislative texts is based on this type of disposition:

(23) Tätä kaikki asianomaiset noudattakoot. (Example cited by [START_REF] Hakulinen | Iso suomen kielioppi [Comprehensive Finnish Grammar[END_REF]Hakulinen et al. : § 1667.) .) 'This must be respected by all parties concerned.' tätä kaikki asianomaiset noudatta-koot DEM.PART all party.concerned.PL respect-JUSS However, in the data analyzed for the present study, the referent of the jussive form was not necessarily a potential actor whose behavior in the situation could be submitted to the speaker's intention. In this type of case, the command cannot be addressed to the referent of the jussive form. In the following two examples, the referent of the jussive form is, first, an inanimate entity (boat) and, second, an unconscious human being. The context of example ( 24)

was described at the beginning of this paper (see example 1). In example (25), the speaker was reporting how people used to take care of someone who had drunk too much alcohol.

( 'they took him away then they-took if he fell outdoors so they didn't leave him there to freeze they took him in some warm shelter let him stay here.'

ol-koo hää tääl be-JUSS 3SG here

Even though the referent of the subject is unable to change their own state in these examples, the speakers are accompanied in the situation by other parties who figure as intentional agents and potential actors. The command can thus be understood as directed at them. In example (24), the speaker (grandfather) addresses the other potential passengers of the boat, indirectly prohibiting the use of the boat by all, including himself. In (25), the unspecified, possibly collective speaker expresses an obligation, involving all the participants present that could affect the referent's location.

At the same time, the permissive reading is not entirely absent in these examples. While the jussive clause is used to obligate the participants present, it also codes a state that is favorable to someone. In ( 24), the directive clause can be understood as liberating the participants from having to move the boat. In (25), the permissive stance is addressed to a momentarily unconscious, but personal and empathy-worthy being who is now protected from the cold.

If the event denoted by the jussive clause cannot be considered as controlled by an intentional agent, whether this is the referent of the jussive form, the speaker or another party, the speaker's intention is foregrounded and an optative meaning emerges (for a similar use of the Estonian jussive, see Metslang and Sepper 2010: 532; see also Scholze 2010: 388 for the Sorbian jussive).

(26) Vallitkoon maailmassamme oikeus, totuus, hyvyys, kauneus ja suurimpana rakkaus, hän sanoi. (FTC, Kaleva 1998[START_REF] Yamamoto | Animacy and reference: A cognitive approach to corpus linguistics[END_REF] 'May justice, truth, goodness, beauty andthe greatest of alllove prevail in our world, he said.'

Vallit-koon maailmassamme oikeus prevail-JUSS world.INE.POSS.1PL justice In this example, the referents of the subject NPs (oikeus,… 'justice,...') are abstract, unintentional entities. On the other hand, the state of affairs coded by the verb vallita ('prevail') is in itself static, in other words, there is no implication of a change that could be caused by someone. As with the examples ( 24) and ( 25), which also include a static verb (olla 'be'), the jussive gives rise to an implication, according to which the state of affairs coded by the verb could, however, be interrupted. The permissive aspect of jussive semantics can be observed in this regard. The directive speech act advocates not only a state of affairs that the speaker presents as desirable, but also a state of affairs that prevails if allowed to do so.

Consequently, the optative meaning produced by the jussive mood does not typically give rise to an expression of personal interest. This type of wish is expressed in Finnish by the conditional mood (Kauppinen 1998: 187-189), as in ( 27):

(27) Ol-isi-pa jo kesä be-COND.3SG-PTCL already summer 'If only it could already be summer' Instead of implying an authority that allows the desired event to take place (or to prevail), the conditional, essentially a mood of epistemic modality in contemporary Finnish, highlights the event as belonging to a possible world, which is parallel to the reality constructed in the discourse. The division of labor between the jussive and the conditional in Finnish optative clauses appears to be comparable to that observed in Sorbian by Scholze (2010: 388, 390).

The types of jussive clauses illustrated in this section foreground the speaker's intention toward other parties' actions on the world. In other words, they foreground how things should be according to the speaker's will while, at the same time, including the idea of allowing a state of affairs to take place. In the next section, the positions have changed: the permissive stance is dominant.

Permission and decision-making

The permissive reading occupies the foreground when, in addition to the speaker, another intentional agent is present in the context and the action denoted by the jussive form is understood as either desired by this other agent or generally favorable for them. The speaker's intention appears in the form of conforming to the realization of the event. This is illustrated in example ( 28), where the speaker's attitude toward smoking is expressed, and in ( 29), where the informant reports the words of one of her former employers, for whom she had worked as a servant in her youth. The extract concerns the possibility of the servants going out and the attitudes of their employers toward it. ( 28 'because in Pusa the wife was also of the type that she didn't really like it but since the master always just said that it didn't matter just let them go they can / should go out as much as they like as long as they are home when they are needed that it didn't matter for him that as far as he was concerned they could go out that he wouldn't stop them and.'

anta men va et men-kkö vaa nim paljon ko kon kerkkevä let.3SG go PTCL PTCL go-JUSS PTCL as much as as can.3PL

In ( 28), the action expressed by the jussive form ('smoke') is presented as being in accordance with the intention of the referent 'smoker'. The will is made explicit by the adverb vapaasti ('freely', 'according to his/her/their own will'). The speaker shows his or her alignment to the realization of the action. In ( 29), the will of the potential executor of the action of going out is implied by the third person plural verb form kerkkevä (inf. keretä 'to be able to, within the limits of time'), in other words achieving the temporal landmark entailed by keretä, with as much going out as possible, presupposes that the agent has a tendency toward the action of going out. Furthermore, the modal verb saada ('could/should', see section 2.2) in the clause et hänem pualestas saa men vaa ('that as far as he was concerned they could go out') foregrounds the permissive reading due to the adverbial hänem pualestas ('as far as he was concerned'), which leaves the conceptual path open for another participant to pass through ('not imposing a barrier').

Although the events in examples ( 28) and ( 29) are in line with the intention of the potential executor of the action, the jussive clauses cannot be interpreted as mere consents.

These permissions are, as were the obligations analyzed in the previous section, situated in a context of decision-making. By expressing his or her conformity to the realization of the event initiated by another participant, the speaker sets up a norm, which is addressed to parties who are not the potential executors of the action denoted by the jussive form, but who have their say in the matter. In example (28), this party is the people who could potentially prevent the smoker from acting "freely" and, in (29), it is the housewife who is not in favor of the young employees going out.

In (29), the preceding construction anta men va ('just let them go') with the modal permissive verb antaa ('let') is revealing. The construction includes the so-called "zero person", in other words the position of a nominal element with unspecified referent is left empty. In (29), the position of the syntactic subject is open (Ø antaa men va 'Ø just lets them go'), and the verb takes the third person singular form accordingly. By using the zero person construction, the speaker leaves the subject position ("the permitter") of the clause open, allowing the other participants of the speech situation, who potentially have control over the event, to place themselves in this position (see [START_REF] Laitinen | Zero person in Finnish: A grammatical resource for construing human reference[END_REF]). Von Waldenfels (2012: 195-196) considers this type of permissive construction, with the verb antaa and the zero person, to be a special type of imperative clause, which is a demonstration of the illocutionary force of the construction (for the syntax and semantics of antaa, see [START_REF] Leino | Antaa sen muuttua: Suomen kielen permissiivirakenne ja sen kehitys [Let it change: The Finnish permissive construction and its history[END_REF][START_REF] Leino | Frames, profiles and constructions: Two collaborating CGs meet the Finnish Permissive Construction[END_REF].

In both examples, we can thus recognize the modal necessive meaning of the jussive behind the highlighted permissive reading. 16

Dynamic necessity and the non-intervention of the parties present

The third group of jussive occurrences, where permission and obligation are inseparable, consists of clauses where the jussive codes a necessity imposed on an agent by the circumstances. These clauses do not produce a directive speech act, but a modal expression of necessity. The jussive clause figures as part of a complex construction in which the initial member denotes a state of affairs having taken place and the second, the jussive clause, is a necessive consequence of it, in other words a situation that the agent must comply with (see Birjulin and Xrakovskij 2001: 47-48). At the same time, the jussive clause expresses an event that the other participants of the situation let happen.

All occurrences of this type came from the South Eastern dialects of Finnish data. These dialects belong the larger category, composed of the Eastern dialects, which generally display a particularly rich variety of imperative clause usage compared with the standard language (see Forsberg, forthcoming). This type of jussive is illustrated in example (30), where the speaker describes a typical situation of receiving guests in a house, and in (31), where the speaker recounts a Christmas celebration of the past.

(30) siit ol piirakat paistettu ja pullat ja rieskat ja ne kannettii kokonaa pöyväle ja ottakoo puuko jokkaine taskustaa mil ne söi ja lusikat ol talo puolesta. (SA, Nuijamaa.)

'the pasties and buns and bread were baked and all of it was put on the table and everyone would have to / was left to take their knife out of their pocket to eat and the spoons were provided by the house.' ja otta-koo puuko jokkaine taskustaa mil ne söi and take-JUSS knife everyone pocket.ELA.POSS.3SG/PL REL.ADE 3PL eat.IPF.3SG/PL (31) kell-ol' viinaa se joi viinaa ja mitäs siinä ol'i kell-ei ollu ni sitte olkoo juomatta. (SA, Sortavalan mlk.)

'he who had liquor drank liquor and that's it he who didn't have it well then he had to stay without drink / he was left without' kell-ei ollu ni sitte ol-koo juomatta REL.ADE NEG.3SG be.PST.PTCP PTCL PTCL be-JUSS drink.INF.ABE

The events coded by the jussive clauses, 'everyone would have to / was left to take their knife out of their pocket' and 'he had to stay without drink / he was left without', cannot be considered as particularly favorable from the subject referent's point of view in either of the examples. The permissive meaning of the jussive is therefore not interpreted as the speaker conforming to another intentional agent's will, but as the other participants' nonintervention, or passiveness, in the situation. As for the meaning of obligation, due to the generic-habitual context, it does not give rise to a proper directive reading. 17 The clause is understood as a description of the dynamic generic necessity arising from circumstances as opposed to an intentional agent. 18

Conventionalized uses

In this section, I address a series of jussive constructions that have been grammaticalized or lexicalized to different degrees and point out their semantic link to the modal binarity of the jussive analyzed in the previous section.

The first type of conventionalized constructions is the concessive jussive clauses. It has been pointed out that expressions of permission are likely to develop into concessives (Bybee et al. 1994: 227; see also Haspelmath and König 1998: 598-599). 19 In complex constructions, permissive meaning conveyed by the jussive in main clause position, based on the situation of interaction and the agency of the participants, is modified so that it turns into an interclausal relation overriding the contradiction between events, which are, by implication, displayed as exclusive. In other words, it is not about the speaker conforming to the will of another intentional agent, but about the absence of opposition between events, which, by definition, are assumed to be opposed (Peltola 2011: 188;Duvallon andPeltola 2013, 2014).

The interclausal link produced by the permissive meaning of the jussive can be qualified either as an alternative concession, non-factual by its truth value, or as a simple concession, involving factual events. Example (32) includes an alternative concessive clause. The concessive reading is founded on a situation where several elements are displayed in the subordinate clause as taking the place of the referent alternatively, with no consequence in respect of the realization of the main event. These elements can be presented in the form of a list, a scale or as alternatives that are in mutual contradiction (see Peltola 2011: 185-190). In (32), the concessive reading depends on free-choice quantification (mitä tahansa 'whatever') (see [START_REF] König | Conditionals, concessive conditionals and concessives: Areas of contrast, overlap and neutralization[END_REF].

Example (33) contains a simple concession, sometimes called "real concession", since no explicit alternatives to the state of affairs are presented. However, due to the nonspecific temporal semantics of the jussive, the state of affairs is displayed as a theoretical possibility (see [START_REF] Leech | Meaning and the English verb, 2nd edn[END_REF][START_REF] Leech | Meaning and the English verb, 2nd edn[END_REF]: 113-116) rather than as a fact (see Section 2.1.3 above):

(33) Olkoon teatteri ressukka, mutta maailmanensi-iltoja tulee viisi. (FTC, Aamulehti 1999.)

'Though it is / it may be a poor little theater, there will be five world premieres.'

Ol-koon teatteri ressukka, mutta maailmanensi-iltoja tulee viisi be-JUSS theater poor but world.GEN.premiere.PL.PART come.3SG/PL five

The concessive jussive clauses are adverbial because they denote the circumstances under which the event expressed by another clause takes place (see Cristofaro 2003: 155). In functional terms, they can thus be regarded as subordinate to this other clause.

In the Eastern dialects of Finnish, the concessive relation between events can furthermore be coded by the concessive conjunction vaik(ka) ('even though'), even in the case of a jussive clause ( 34 The co-occurrences of the clause-initial vaik(ka) and the jussive are the result of their semantic similarity: they both code theoretical alternatives (see Duvallon andPeltola 2013, 2014). They also prove that this type of jussive form is to be interpreted in relation to the accompanying clause. 20It is possible that the jussive displays a greater facility to occur in subordinate clauses than the second person imperative forms. Due to its third person reference, the jussive does not activate the polarity between the first and second person. As the directive speech act can be viewed as being addressed prototypically from the speaker to the listener (see, e.g., Birjulin and Xrakovskij 2001: 5-8, according to whom all imperative clauses other than second person are non-canonical), jussive semantics may be more receptive to being reoriented from speech-act participant to interclausal relations. 21 The conventionalized use of the jussive discussed below demonstrates that, in certain regions, the jussive has undergone further semantic bleaching in its interclausal, adverbial position.

These jussive uses are also a particular feature of the Eastern dialects. The jussive itself appears to have developed into a marker of adverbial elements in these regions, as demonstrated in ( 35).

(35) no siin ol' tanssipaekka siinä ko ol'ni sano että hyö rupes sitte olkoo kellarikatollev vae mi-johokii ni hyö rupes kortipelluusee. (SA, Mikkelin mlk.)

'well there was a dancing place there was-so he said they started OLKOO on a cellar roof or wh-somewhere so they started to play cards.' hyö rupes sitte ol-koo kellarikatollev vae mi-johokii 3PL start.IPF.3SG/PL PTCL be-JUSS cellar.GEN.roof.ALL or Q-somewhere ni hyö rupes kortipelluusee PTCL 3PL start.IPF.3SG/PL card. GEN.play.ILL In (35), the circumstances coded by the jussive clause olkoo kellarikatolle vae mi-('OLKOO on a cellar roof or wh-') do not strictly speaking correspond to another event, but rather to a spatial frame within which the event coded by the main clause takes place. This frame is nonspecific by its reference because the permissive meaning of the jussive allows more than one referent to alternately take the place of the subject. The list of possible referents, the components of which are coordinated with the disjunctive conjunction vai ('or'), is left open with the indefinite pronoun johokii ('somewhere'). In this context, the nonspecific reference is understood as a difficulty in recalling the name of the place.

In the data, this type of construction also expressed temporal circumstances (36) or modified the representation of one of the participants (37).

(36) vaik olkoo nykyjeäkii ni kyl niiss [kaloissa] In example (36), the jussive clause (vaik olkoo nykyjeäkii 'even OLKOO today') serves to construe a temporal setting that covers an entire timescale extending to the present moment.

The proposition 'the fish have their own particular smell' is held to be true for all points on that scale. In examples ( 35) and ( 36), the jussive clause verb (olla 'to be') is lexically weak.

In example (37), the speaker is describing the old custom for proposing marriage, according to which the proposal was made not by the groom, but by some older people, who also offered money to the young woman. In examples (35) to (37), the semantic process is the same as that in the concessive clauses, in other words the permissive meaning of the jussive takes a syntagmatic, relational dimension.

In contrast to the concessive clauses in ( 35) to (37), the jussive clauses do not denote an event but a spatiotemporal setting or the range of potential participants of the event coded by the main clause. They include very few constituents: only the jussive verb with weak lexical contribution and the elements denoting the potential subject of the jussive verb. These jussive clauses do not therefore seem like prototypical subordinate clauses. The permissive meaning of the jussive operates not so much at interclausal level, as in the case of the concessive clauses, but within the main clause, allowing the integration of the nonspecific reference. 22Using the jussive in concessive clauses and as a marker of a nonspecific adverbial element highlights the permissive modal meaning of the mood. These jussive forms denote that it is possible for seemingly contradictory events to co-occur (examples 32-34) or for the event of the main clause to take place despite the (non-specified) circumstances (examples 35-37).

The next two groups of conventionalized jussive constructions allow the necessive side of the jussive semantics to come to the fore. In standard Finnish, the passive voice of the speech With this kind of construction, the speaker guides the interlocutor. The construction can thus be considered a kind of command (see also the use of the jussive in legal contexts, example 23, above). Furthermore, the jussive occurs in a number of conventionalized constructions of affect. Some examples of these are presented in (39).

Onneksi

ol-koon happiness.TRANSL be-JUSS It seems to be characteristic of jussive forms generally in languages to appear in this type of affective, conventionalized clause. The Estonian jussive displays comparable uses in curses and swear words, such as in And-ku jumal andeks! 'May god forgive!' (Metslang and Sepper 2010: 546). Malygina (2001: 274) reports that some Old Hebrew jussive forms are present in Modern Hebrew in conventionalized expressions like lu yehi ('let it be') and texi yedidut ('long live friendship').

Discussion

We have seen, in the previous section, that the jussive allows speakers to express the interests and points of view of two or more parties simultaneously: what is one's necessity is another's possibility. The fact that the two modal meanings, presented as opposite ends of the modal axis, can meet in the uses of a linguistic element shows the twofold nature of permissions. In order to allow something, there has to be another agent's will or some other form of necessity that pre-exists. 23It should be stressed that this double modal meaning should not be analyzed as causing a lack of clarity in the discourse. [START_REF] Viberg | Language-specific meanings in contrast: A corpus-based contrastive study of Swedish få 'get[END_REF]Viberg ( : 1427) ) remarked that uses of the Swedish modal verb få, otherwise semantically vague, are restricted to permissive meaning in legal context. This is also true for the equivalent Finnish verb saada. As for the uses of the jussive in a similar context, the meaning of obligation comes to the fore (see [START_REF] Hakulinen | Iso suomen kielioppi [Comprehensive Finnish Grammar[END_REF]: §1667; see also example [23] above). Formal language registers, such as legal language, do not tolerate the twofold modal meaning under discussion here for understandable reasons.

However, in more spontaneous language use, such as that represented by the data in this study, there is no reason to think that the interlocutors consider the coexistence of two modal readings as problematic. Rather, the simultaneous presence of permission and obligation represents the dialogical nature of modal elements and illustrates the fact that grammatical constructions have their foundation in human interaction. Following Linell's (2012: 111) definition of dialogism (or contextualist interactionalism), the binary modal meaning of the jussive reveals the speaker's "understanding of self, others and the world". Semantic vagueness takes the form of discursive openness as several points of view on the event are left available.

The situation where the two modal poles stay simultaneously active can therefore be regarded as a discursive resource.

Conclusion

In this paper, I have regarded the Finnish jussive mood as a meeting ground for the modal meanings of permission and obligation and examined its semantics and use. I have argued that the two readings are simultaneously present in the interpretation of jussive clauses, which gives rise to various positionings of intentional agents in regard to each other and to the event that potentially takes place. The twofold modal meaning of the jussive can be considered a discursive resource: it allows more than one point of view on the event to be expressed. Due to its third person reference, the jussive inherently dissolves the unity of perspective from which the event is viewed, based on the polarity between the speaker and the listener. As a deontic modal expression, it introduces another intentional agent in addition to the two speech act participants.

The present paper has aimed to illustrate the variety of modal readings afforded by jussive semantics, ranging from those where necessive modality is foregrounded to those where the meaning of permission is dominant, but where the presence of the opposite pole is always in evidence.

I have pointed out some differences between the two types of data used, drawing attention in particular to the richer variety of uses of the jussive in the Eastern dialects of Finnish as compared with the standard language represented by the newspaper data. Social and regional variation in the uses of the jussive remains, however, to be investigated using a larger dataset.

In light of the jussive semantics, I have shown that linguistic modality is not merely a structure of mutually exclusive categories and that the inverse modal meanings open up different perspectives on the event and reflect the dialogical aspect of language.

  demonstrated this correspondence between få and saada in his contrastive study investigating the translations of få into English, Finnish, French and German. Apart from få, the verb saada was the only marker in his data to display the binary modal meaning (on the types of modality expressed by the Finnish verb saada and its equivalents in other Balto-Finnic languages, seeKeyahov and Torn-Leesik 2009: 371-374). Modal verbs covering the two extremes of deontic modality simultaneously have also, however, been found in other languages.[START_REF] Laitinen | Pitääkö vai saakomodaaliverbin kaksoissidos [Modal verb in a double bind[END_REF] presents a similar analysis on the Inari Sámi kolgađ and Davidsen-Nielsen (1990: 187) and van der Auwera et al. (2004) on the Danish måtte. Furthermore, the causative verb lassen is used in modern German for coercive and permissive causation alike (see Hans-Bianchi 2012). Its Finnish equivalent antaa covers factitive and permissive causation in a similar way (see vonWaldenfels 2012: 208-209, 212-214).15 As for modal affixes and verb constructions, a comparable vagueness is displayed, for example, by the negative imperatives formed with the marker -nghit-in Asiatic Eskimo(Vaxtin 2001: 141), by the German sein + zu infinitive construction (van der Auwera and Plungian 1998: 101) and by the Russian dative-infinitive construction (in the context of negation)(Fortuin 2005: 55-56).Semantic vagueness does not only apply to the meanings of obligation and permission in the languages of the world.[START_REF] Van Der Auwera | Acquisitive modals[END_REF] showed that, within the Indo-European and Finno-Ugric languages of Northern Europe, there is a concentration of modal markers expressing, on the one hand, acquisition and, on the other, modal possibility, including permission and, in many cases, capacity. The Estonian verb saama ('get'), for example, marks not only participant-external meanings, such as possibility due to the circumstances or authorization coming from another intentional party (see the semantics of the 'get' verbs analyzed above), but also participant-internal ability (seevan der Auwera et al. 2009: 286-287;

( 32 )

 32 Lukekoon valmentajan ohjelmassa mitä tahansa, on levättävä silloin kuin keho niin sanoo. (FTC, Aamulehti 1999.) 'Whatever the coaching program says, you have to rest when your body tells you to.' Luke-koon valmentajan ohjelmassa mitä tahansa say-JUSS coach.GEN program.INE whatever

  The main clause verb (käydä 'to pass') is repeated in the jussive clause. The lexical contribution of the jussive verb is thus minimal here too. As in the previous examples, the jussive clause conveys a nonspecific reference. Due to the permissive meaning of the jussive, the referents of the two elements coordinated by the disjunctive elikkä ('or') can potentially take the position of the subject.

  1999: 26). 12 This is illustrated by example(21), where the speaker reports how her niece(Milja) and the niece's fiancé (Martti) ask her to come and visit them: 13 (21) ku tul' se Milja sulhanekii ja patistiit minua Rätäkkää(...) se sano miule, Miljakii juoks ni et, et lähtööks vanhaäit tuol ja, et tul't seä vua Rätäkkää kattomaa mei paikkoja ni, no se sulhane se Martti sano voa niin ikään et se o vanhaäiti sen ko lähteköö et sen ku myö tulloa oamul hakem ne tul' Moantakoa (mu hakemoa) ja meä käi siel kattomas siit senkii paika viel. 'then Milja's fiancé came too and they urged me to go to Rätäkkä (…) and he told me, Milja came running too [and asked], is grandmother going and are you coming to Rätäkkä to see our place, so the fiancé Martti also said grandmother should / may come we'll come and fetch [you/her] in the morning they came to Moantaka (to fetch me) and so I got to see that place too.'

	lähtöö-ks	vanha.äit	tuol	ja et	tul'-t	seä vua
	leave.3SG-Q old.mother PROADV and CONJ/PTCL come-2SG 2SG PTCL
	Rätäkkä-ä katto-ma-a mei	paikko-j-a	ni.

PROP-ILL look-INF-ILL 1PL.GEN place-PL-PART PTCL vanha.äiti sen ko lähte-köö old.mother PTCL PTCL leave-JUSS The jussive clause vanhaäiti sen ko lähteköö ('grandmother should / may come), assigned to the niece's fiancé, Martti, simultaneously codes an invitation addressed to vanhaäiti ('grandmother') and an alignment to the initiative that Milja has taken previously, namely the request denoted by the two interrogative clauses (lähtööks vanhaäit […] tul't seä vua Rätäkkää […] 'is grandmother going […] are you coming to Rätäkkä […]'). The third person reference

is present not only in the jussive clause, but also in one of the interrogative clauses. As it is clear from the context that the three participants share the same spatiotemporal setting, the third person forms are conceived as referring to a participant present in the situation who is a potential next speaker (see

Sacks 1992: 573; Seppänen 1998: 126-127)

.

14

it the groom's father or someone else.'

  o oma hajusa kuka ei tykkeä kalahaisust nis se ei mäk koko kala, puot'ii. (SA, Taipalsaari) 'even OLKOO today, well they [the fish] have their own particular smell if someone doesn't like the smell of the fish well they just won't go to the fish shop.' nii sellasta ol sillo ko miekii muistamaa rupian nii, ne käi rahoomassa siitt että, käyköö siit sulhase isä elikkä joku muu. (SA, Nuijamaa) 'so that's what it was like from the time that I can remember so, they passed and paid and, be

	vaikk		ol-koo nykyjeä-kii ni kyl nii-ss	o
	even.though be-JUSS today-CLT PTCL PTCL DEM.PL-INE be.3SG
	oma haju-sa
	own smell-POSS.3SG/PL
	(37) ne kä-i	rahoo-ma-ssa siitt että käy-köö	siit sulhase
	3PL pass-PRET.3SG/PL pay-INF-INE PTCL PTCL pass-JUSS PTCL groom.GEN
	isä	elikkä joku muu.
	father or	INDEF other

  act verbs in the jussive has conventionalized into a rhetorical means by which the speaker can anticipate and refer to his own speech act. This is a function also displayed by the passive forms of the same group of verbs in the present indicative (see[START_REF] Makkonen-Craig | Connecting with the reader: Participant-oriented metadiscourse in newspaper texts[END_REF]. Consider the JUSS COMP woman.PL be.able.to.go.IPF.3PL

	following example:
	(38) Mainittakoon, että naiset pääsivät seuran jäseniksi vasta vuodesta 1966 lähtien. (FTC,
	Turun Sanomat 1999.)
	'Let me say in passing that women were accepted as members of the association only
	from 1966 onward.'
	mainit-ta-koon	että naiset	pääsivät
	mention-PASS-

This presupposes the adoption of the broad definition of imperative clauses, according to which any participant (as opposed to just the addressee) can perform the function of the agent. Thus, the category of imperative clauses is not limited to second person imperatives (seeBirjulin and Xrakovskij

2001: 5-8).

The name of the subcategory of corpus corresponds to the name of the newspaper, which is followed by the year of publication.

The extracts of dialect data analyzed in this paper are followed by the name of the town or village represented by the informant.

For a more exhaustive presentation of the Finnish verbal system, see[START_REF] Tommola | Mood in Finnish[END_REF].

Note that, in Estonian, the third person imperative form in the singular and plural is, however, homonymous with the jussive (for a discussion of the status of the Estonian jussive as a mood, seeMetslang and Sepper 2010: 533- 534). The difference between the Finnish and Estonian jussives is that the latter can appear with first and second person pronouns: ma/sa/ta/me/te/nad istu-gu '1SG/2SG/3SG/1PL/2PL/3PL sit-JUSS'(Erelt and Metslang 2004: 167).

 6 In non-standard variants, the jussive is also marked by several other affixes.

As van der Auwera et al. (2009: 275) pointed out, however, the distinction between permission authorized by the speaker and by some other party is not necessarily always clear.

Permission seems to be close to directive acts like invitation and advice in many languages (see, e.g.,Nasilov, Isxakova, Safarov and Nevskaja 2001: 203; Ogloblin 2001: 235; Spatar 2001: 476). All three directive types are characterized by the central role of the other agent's will in the interpretation of the clause. The event in question is considered, in principle, as wanted by or otherwise favorable to the other agent.

Third person forms cannot thus be described as referring only to an "outside person not included into [sic] the act of communication" (cf.Birjulin and Xrakovskij 2001:19).

For a more detailed analysis of the extract, seePeltola (2011: 171-174).

For a discussion of the referential complexity of imperative clauses from a typological point of view, see van der Auwera,[START_REF] Van Der Auwera | A semantic map for imperative-hortatives[END_REF].

On the origins of the binary modal meaning of the verb antaa, seeLeino (2012: 239-242).

Furthermore, example (29) includes an occurrence of another permissive marker, the modal verb saada ('get'). Its semantic similarity with the jussive is discussed in Section 2.2.

See Nuyts et al. (2005: 27-29), for a comparable series of examples of permissive expressions in a generic context.

Note that examples (30) and (31) offer another illustration of the jussive associated with the past tense, expressing past events (see the discussion on deontic modalities and time in Section 2.1.3).

See, however, Souesme's (2009) analysis of the English verb may where the permissive meaning is not considered the source of the concessive reading.

See Metslang and Sepper (2010: 546-547) for a similar evolution (from permission to concession) of the Estonian permissive particle las (< laksma 'let'), andScholze (2010: 384) for a comparable concessive use of the Sorbian jussive.

See alsoScholze (2010: 388) for an example of the Sorbian jussive mood in a completive clause.

The jussive is not the only permissive element in the Finnish language to have undergone semantic bleaching. The second person imperative forms of the permissive modal verb antaa ('let') have grammaticalized into a discursive marker, announcing the next action of the speaker, as described in vonWaldenfels (2012: 194-195, 204-205).

On the other hand, while what is obligatory is permitted, the converse is not true(von Wright 1951: 4; Lyons 1977: 838).

Acknowledgements

The author would like to thank the two anonymous reviewers for their valuable comments and suggestions.


Jacques Fontanel

Ivan Samson

Fanny Coulomb

come


Boyin Ding
email: boyin.ding@adelaide.edu.au

Pierre-Yves Wuillaume

Fantai Meng

Aurélien Babarit
email: aurelien.babarit@ec-nantes.fr

Benjamin Schubert

Nataliia Sergiienko

Benjamin Cazzolato

Comparison of wave-body interaction modelling methods for the study of reactively controlled point absorber wave energy converter

INTRODUCTION

Ocean waves are a huge resource of renewable energy for utilisation. Wave energy converter (WEC) devices are being developed to enable capture of this energy resource. In the late 1980s, the principle of extraction energy from waves was studied [START_REF] Falnes | A review of wave-energy extraction[END_REF] and it showed that reactive control can increase significantly wave power extraction for a heaving point-absorber. Since then, studies on the control strategies and their implementations have been a focus in the field of wave energy research [START_REF] Ringwood | Energy-maximizing control of wave-energy converters[END_REF].

Majority of the wave energy control studies used linear potential flow theory and Cummins equation as the basis for modelling hydrodynamics arising from wave-body interaction, which is essential for the implementation of control simulation as well as for the formulation of model-based control strategies [START_REF] Penalba | A review of wave-to-wire models for wave energy converters[END_REF]. Although this simplifies/linearises the control problem as well as speeds up the simulation process, the utilisation of linear solver (which assumes that the wave steepness and body motion are both small) contradicts the large motion arising from the reactively controlled wave energy converter and thus does not ensure the fidelity of the control simulation results in medium to large wave conditions. On the extreme opposite, the Navier-Stokes equation based CFD captures the full nonlinear hydrodynamics in the wave-body interaction problem leading to high fidelity simulation results regardless of the system operational conditions, however, is barely used in the study of wave energy converter control due to its high computational requirement. Compromise between the linear method and the Navier-Stokes solver also exists [START_REF] Wuillaume | Numerical simulation of installation operations for offshore wind farms[END_REF]. A typical example is the weak-scatterer potential flow method proposed for seakeeping analysis of ship with forward speed [START_REF] Pawlowski | A theoretical and numerical model of ship motions in heavy seas[END_REF], which is formulated based on the assumption that the perturbation wave field generated by the body oscillation is small compared to the incident wave field, such as the free surface conditions can be linearised at the incident wave elevation level. The weak-scatterer method takes into account the unsteady and nonlinear hydrodynamic loads associated with dynamic wavebody interaction as long as the aforementioned assumption is satisfied and that viscosity effects remain negligible. However, it remains questionable if the weak-scatterer method is suitable for solving wave energy converter control problem where large perturbation wave field is expected given the large resonant motion of the body. A further simplified version of the weak-scatterer method is the body-exact potential method that assumes the free surface conditions can be linearised around the mean free surface elevation 𝑧 = 0. This solver was proposed to account for the body motion induced nonlinearities but is only valid when small steepness waves are present. It is a compromise between the weak-scatterer method and the linear method.

The proposed study intends to conduct a comparison study on the aforementioned four wave-body interaction modelling methods in terms of their fidelity in solving the reactive control problem of a submerged point-absorber (PA) WEC.

WAVE-BODY INTERACTION MODELLING METHODS

Table 1 summarises the main differences between the four wave-body interaction modelling methods. 1) Navier-Stokes equation (CFD) solver: Navier-Stokes equations are a set of partial differential equations that describe the motion of fluids as a relationship between flow velocity (or momentum) and pressure. For the incompressible sea water, the Navier-Stokes equations can be written in the general form as:

𝜌( 𝜕𝐮 𝜕𝑡 ⁄ + 𝐮 • ∇𝐮) = -∇𝑝 + ∇ • (𝜇∇𝐮) + 𝐟 (1a)
∇ • 𝐮 = 0 (1b) where 𝐮, 𝜌, 𝑝, 𝜇 and 𝐟 are the velocity vector, density, pressure, dynamic viscosity and external force (e.g. gravity force) and ∇ is the gradient operator. Solving Equation (1) stepwise across the computational domain of the numerical wave tank under boundary conditions and integrating the total stress over the wetted body surface 𝑆 𝐵 (𝑡) result in the total hydrodynamic force acting on the body [START_REF] Meng | Numerical simulation of a submerged spherical point absorber with asymmetric mass distribution[END_REF]. The advantage of CFD solvers are that they are not based on any linearisation assumption, take into account the real fluid viscosity, can accommodate turbulence effects and other nonlinear phenomena that may occur during a simulation. However, these benefits come at a cost of high level of complexity and very high computation time relative to linear models. In this study, the OpenFOAM package (e.g. OLAFOAM and interFoam utility) forms the CFD solver (specifically the Reynold-averaged Navier-Stokes model) as described by [START_REF] Meng | Numerical simulation of a submerged spherical point absorber with asymmetric mass distribution[END_REF].

2) Weak-scatterer potential flow (WSP) solver: The potential flow theory was established based on the assumptions that the fluid is irrotational, incompressible and inviscid. Without considering the viscosity and turbulence, the potential flow theory introduced the velocity potential 𝜙, the only one scalar function that is necessary to compute the three dimensional fluid velocity. Thus, the velocity potential can be evaluated using a boundary element method and the total pressure can be solved from the Bernoulli's equation [START_REF] Wuillaume | Numerical simulation of installation operations for offshore wind farms[END_REF]:

𝑝 = -𝜌 ( 𝜕𝜙 𝜕𝑡 + 1 2 ∇𝜙 • ∇𝜙 + 𝑔𝑧) (2)
where -𝜌𝑔𝑧 is the hydrostatic pressure. The total dynamic force acting on the body is then calculated by integrating the total pressure over the instantaneous wetted surface of the body 𝑆 𝐵 (𝑡). Due to the high computational demand associated with the fully nonlinear potential flow method in solving the real varying intersection curves between the free surface and bodies, decomposition of the velocity potential and the wave elevation into incident and perturbed quantities were applied and the weak-scatterer hypothesis was proposed [START_REF] Pawlowski | A theoretical and numerical model of ship motions in heavy seas[END_REF]. It assumed the perturbed quantities are small compared to the incident quantities:

{ 𝜙 = 𝜙 𝐼 + 𝜙 𝑃 𝜙 𝑃 = 𝒪(𝜙 𝐼 ) . (3)
In this case, the free surface boundary equations are linearised around the known incident free surface elevation 𝑧 = 𝜂 𝐼 (𝑥, 𝑦, 𝑡). Thus, the perturbed waves are not required to be meshed which largely reduce computational demand. Due to the free surface conditions, wave breaking cannot be modelled. In this study, the WS_CN numerical tool as described in detail by [START_REF] Wuillaume | Numerical simulation of installation operations for offshore wind farms[END_REF] will be used as the WSP solver.

3) Body-exact potential flow (BEP) solver: The potential flow theory based solver can be further simplified under small wave conditions (e.g. wave steepness, 𝜖 ≪ 1). Thus, the free surface conditions can be linearised around the mean surface elevation 𝑧 = 0. This forces the free surface mesh remain planar, which enables a faster mesh convergence and reduction of computing time. The pressure is integrated over the wetted body surface 𝑆 𝐵 (𝑡) subject to "body-exact" motion and delimited by the mean wave elevation. In the WS_CN numerical tool, an option of linearising the free surface conditions around the mean surface elevation exists and thus the WS_CN numerical tool can be configured as the BEP solver for use in this study.

4) Linear potential flow (LP) solver:

The potential flow theory based solver can be simplified to its neatest form, by assuming that wave steepness, 𝜖, is small and the body undergoes small amplitude motion, 𝐴 𝑚 . Consequently, the free surface conditions can be linearised around the mean free surface elevation 𝑧 = 0 and the body meshes are fixed at the rest position of the body. This leads to a linearised model, where the perturbed component can be further decomposed into a diffraction component and a radiation component:

{ 𝜙 = 𝜙 𝐼 + 𝜙 𝐷 + 𝜙 𝑅 𝜖 ≪ 1, 𝐴 𝑚 ≪ 1 . ( 4
)
The elementary problems for these velocity potentials are solved and the total hydrodynamic force is obtained by summing the excitation force and the radiation force. The linearised model can be solved either in the time domain [START_REF] Cummins | The impulse response function and ship motions[END_REF] or in the frequency domain, with hydrodynamic functions/coefficients (e.g. added mass, radiation damping and excitation force) pre-calculated using boundary element solver (e.g. WAMIT, NEMOH, Aquaplus). Surface piercing (e.g. when a fully submerged buoy pierces the free surface) cannot be modelled in this case given the linearised surface and body conditions. In this study, a frequencydomain based linear solver is applied [START_REF] Ding | Enhancing the relative capture width of submerged point absorbing wave energy converters[END_REF].

Table 1. Main differences between the four wave-body interaction modelling methods

Linear

CASE STUDIES

Fig. 1 shows the test case, a fully submerged heaving PA WEC with parameters defined in Table 2. A submerged PA was selected since [START_REF] Sergiienko | Three-tether wave energy converter: hydrodynamic modelling, performance assessment and control[END_REF] showed that reactive control plays a critical role in enlarging the absorption bandwidth of this PA system. A spherical buoy was selected to avoid nonlinearities associated with fluid vortices neglected by the potential flow solvers. The power take-off (PTO) was simplified as a combination of a spring, a damper, and a pretension force that counteracts the net buoyancy force. The PA system modelled by the four wave-body interaction methods was tested under regular wave conditions of 0.1m and 1m wave amplitudes and 4 typical wave frequencies, respectively. The PTO spring and damper parameters were optimised in the linear frequency-domain solver so that the PTO damper absorbed power was maximised subject to a body motion constraint of 3m [START_REF] Ding | Enhancing the relative capture width of submerged point absorbing wave energy converters[END_REF]. This mitigated the occurrence of surface piercing which was not accounted for by the linear solver. The optimised PTO parameters were then used by all four wave-body interaction models for a comparison. Quadratic damping was considered as an external force in the three potential flow theory based solvers to account for the drag force neglected by the inviscid fluid assumption. Fluid velocity was assumed to be zero in the Morison force computation due to its negligible influence. Lorentz linearisation was used to convert the quadratic Morison equation into a linearised damping for use in the frequency-domain linear solver [START_REF] Ding | Enhancing the relative capture width of submerged point absorbing wave energy converters[END_REF].

RESULTS

Fig. 2 shows the RAO and power absorption of the heaving buoy at two wave steepness and four typical wave frequencies, output by the four wave-body interaction models. By the time of abstract submission, the CFD solver results at 0.75rad/s had not yet been obtained due to HPC maintenance at the University of Adelaide. At low wave steepness (e.g. 0.1m amplitude), the buoy RAO did not reach the 3m displacement constraint so that the buoy was kept fully submerged during its free motion. In this scenario, the buoy RAO results output by the four solvers reached a good agreement across the frequencies whilst a discrepancy of 14% in the power absorption can be observed between the CFD solver result and the potential flow solver results at 0.85rad/s. The reason behind this discrepancy is under investigation. At high wave steepness (e.g. 1m amplitude), the buoy RAOs were near the 3m displacement constraint, meaning that the buoy moved very closely to the trough of the free surface at its upper stroke so that surface piercing and wave breaking can occur. In this case, both the results output by the BEP solver and the WSP solver diverged from the results of the linear solver (in particular at steeper/higher-frequency waves, with a discrepancy of up to 34%) since buoy motion induced nonlinearities (e.g. those arising from surface piercing phenomenon) became dominant in the system hydrodynamics. The BEP solver and the WSP solver output similar results, with a difference of up to 13%. In general, the WSP solver results were slightly lower than the CFD results, with a discrepancy of up to 8%. The small discrepancy can be attributed to the weak-scatterer hypothesis that disabled the WSP solver from modelling wave breaking. In conclusion, the linear solver showed poor accuracy in modelling reactive control of fully submerged point absorber in high steepness waves, whilst both the BEP solver and the WSP solvers demonstrated acceptable consistency against the CFD solver. More fundamental results (e.g. wave field data and meshing analysis) and new findings are to be shared at the IWWWFB workshop.

  Fig. 1. Submerged heaving PA WEC

Fig. 2 .

 2 Fig. 2. Buoy heave RAO (left) and power absorption (right) under 0.1m (upper) and 1m (lower) amplitude wave

Table 2 . Parameters for the case studies

 2


Luis Guerreiro

Carlos M Fernández-Peruchena

Afonso Cavaco

Martin Gastón

Manuel Collares Pereira

ISES EuroSun

Keywords: Cluster, Day selection, STE (Solar Thermal Electricity), Optimization

The design and optimization of solar power systems requires a detailed knowledge of the dynamic behavior of the meteorology at the site of interest, usually assess by one typical meteorological year (TMY). Even with today's technology, the computational effort to simulate solar energy system performance with one year of data at high frequency (as 1-min) may become colossal if a multivariable optimization has to be performed. This work evaluates a methodology based on cluster analysis for selecting number of individual days able to represent the long-term performance of a solar energy system. This procedure permits to drastically reduce computational effort related to the calculation of a solar power plant energy yield by simulating a reduced number of days from a TMY, facilitating a fast and optimal design of the plant.

Introduction

Concentrating Solar Thermal Power (CSTP) technologies collect and concentrate the Direct Normal Irradiance (DNI) incident on the earth's surface to heat a working fluid and afterward producing electricity through a thermodynamic cycle. The mean power produced by a CSTP system often determines the viability of the Solar Power Project, which is calculated from energy yield simulation computer programs requiring weather data input to drive the optical and thermal models within the simulation tools.

The feasibility analysis of a CSTP plant project requires the estimation of the amount of energy that it will be able to deliver to the grid during its lifetime. A detailed knowledge of the Direct Normal Irradiation (DNI) is a critical point to perform an economical feasibility analysis of these plants, as it is the most determining variable in the final energy yield. This knowledge comprises a deep understanding of the availability and dynamics of the solar resource over different temporal scales (intraday, day, month, year) [START_REF] Vignola | Building a bankable solar radiation dataset[END_REF]. To achieve this, long time series of meteorological data are usually condensed into shorter series that typify the meteorological conditions at a specific location with the aim of data volume reduction and speedingup of energy system simulations, considered as representative of the location of interest.

Currently, the typical year approach is by far the most widely used among the scientific and industry communities for the design and optimization of solar power plants. These datasets hold 8,760 hourly meteorological values that typify conditions at a specific location throughout a longer period. Accordingly, simulations are usually performed using one hour simulation steps, either with steady state models or somehow taking into account system dynamics to more accurately simulate the performance of the plant. Also, worst cases of solar resource availability are often analyzed in order to ensure the viability of the project. Frequently, these worst cases are evaluated by probability of exceedance scenarios, which provide an estimate of electric generation output that the solar resource consultant expects to be exceeded in any given year over the life of the debt with 90% confidence (P90) and 99% confidence (P99) (C.M.F. [START_REF] Peruchena | A clustering approach for the analysis of solar energy yields: A case study for concentrating solar thermal power plants[END_REF].

TMY approach seems to be appropriate for rather detailed simulations of a specific solar power plant. Notwithstanding, DNI exhibits a great variability at high-frequency due to the dynamic effects of passing clouds, which is a key issue in the design and performance analysis of a CSTP system, given its nonlinear response to DNI caused by various thermal inertias due to their complex response characteristics [START_REF] Fernández-Peruchena | Increasing the temporal resolution of direct normal solar irradiance series in different climatic zones[END_REF]. DNI series of sub-hourly resolution (in the range of 1 to 10 minutes) permit an accurate modeling and analysis of transient processes in some CSTP technologies. For example, parabolic troughs with direct steam generation could be particularly sensitive to the cloud transients [START_REF] Eck | Dynamics and control of parabolic trough collector loops with direct steam generation[END_REF][START_REF] Montes | Performance of a direct steam generation solar thermal power plant for electricity production as a function of the solar multiple[END_REF], and, therefore, better analyzed using DNI series with frequency resolutions much lower than 1-h [START_REF] Meyer | Recommendations for bankable meteorological site assessments for solar thermal power plants[END_REF]. This kind of simulations provides more accurate representation of the plant performance at the cost of larger computational effort leading to longer simulation times. Thanks to the powerful computers currently available, these transient simulations are being used not only for detailed simulations of the short term performance of the plant to improve the design and operation of specific aspects of the system, but also for the energy yield estimation over long periods of the plant (e.g. year simulation or even multi-year simulations) for a specific final plant design.

During the optimization of the large number of plant parameters before a final design is reached, a huge number of simulations are required. The computational effort to simulate a CSTP plant performance with 1-year series at high frequency (as 1-min) may become colossal if a multivariable optimization has to be performed. To overcome this problem, several approaches have been presented for reducing or condensing the data, as the Short Reference Year (SRY) [START_REF] Hallgreen | Short Reference Year, SRY[END_REF], which divides the calendar year into periods. However, in this approach, the selection of the representative days is left to the designer expertise, or they are selected emblematic days like the solstices. More recently, a novel approach based on cluster analysis has been proposed to optimally select individual days able to represent meteorological conditions at a site (Carlos M. Fernández [START_REF] Peruchena | A clustering approach for the analysis of solar energy yields: A case study for concentrating solar thermal power plants[END_REF]. The goal of this contribution is to apply this methodology in a location with high-quality and long term validated measurements, in order to evaluate if selected days can represent the performance of a CSTP plant throughout the complete year.

Experimental data and method

Experimental data

A 12-year series of hourly solar irradiance and meteorological parameters measured in Evora, Portugal by the University of Évora has been selected for this study. Table 1 below presents details about the location of the station, its pyrheliometer and the climatic conditions of the station location, according to the Köppen-Geiger classification [START_REF] Peel | Updated world map of the Köppen-Geiger climate classification[END_REF]. The measured data set covers a 12-years period. The data has been recorded every 5 seconds and averaged every 10 minutes. DNI is measured with a Kipp&Zonen Pyrheliometer (model CHP1), a WMO First Class Pyrheliometer with an associated estimated uncertainty at daily scale of <1%. The pyrheliometer is calibrated every 2 years according to the standard ISO9059:1990.

Tab

Energy yield simulations

A 50 MWe Fresnel type power plant without thermal-energy storage and with a primary mirror area of 193.000 m 2 has been designed for Évora, Portugal. The software TRNSYS V.17 (www.trnsys.com) has been used for the estimation of hourly values of the energy produced by this system. TRNSYS is a validated, time-series simulation program that can simulate the performance of photovoltaic, concentrating solar power, water heating systems, and other renewable energy systems using hourly resource data (Wagner, J. M. and Gilman, P., 2011).

Day selection

In this work, a TMY series is generated from measured series available at the location. For selecting specific days of this yearly series, the following parameters have been calculated to characterize individual days: daytime mean temperature; daily cumulative DNI value; sum of the product of DNI ˖ cos (SZA), being SZA the solar zenith angle; a wind-dependent variable that is zero if maximum daytime wind speed is lower than 12 m/s, 2 if percentile 90 of daytime wind speed is higher than 12 m/s, and 1 in any other case.

Cluster analysis comprises a wide variety of techniques for delineating natural groups (clusters) in data sets, so that observations within each group are similar to one another with respect to variables or attributes of interest and the groups themselves stand apart from one another. This technique is useful for summary and discovery:

Summary refers to the reduced representation of the full data;

Discovery refers to finding out patterns into the original data series.

In this work, the objective of applying cluster analysis is summarizing the data, by means of selecting a small number of days to represent the complete year.

Finally, the clustering method used in this work is the K-medoids algorithm, which selects points analyzed as the center of the clusters. Also, the gap statistic method [START_REF] Tibshirani | Estimating the number of clusters in a data set via the gap statistic[END_REF] is used for estimating the number of clusters (groups) in the daily series. The idea behind this technique is to find a benchmark (i.e., a null distribution) and to compare the observed value of W (the within-cluster variability) with the expected value under the null distribution (being large deviations from the mean evidence against the null hypothesis).

Method relevance

The aim of this method, using groups of data as clusters is to enable a faster analysis of a wide range of options when designing a Solar Plant. With today's computer processing capability this might seem outdated. However, engineers that design big plants usually do not have plenty of time to run multiple scenarios and in multiple locations. For that reason, reducing the computing time for one set of data for a specific location is an advantage specially in the pre-design phase. With the cluster analysis the computing effort in time is reduced in a magnitude of 15 to 20 times, thus enabling many other alternatives and configurations to be studied.

Results

Optimal number of days

In fig. 1 it is represented the gap statistics for the TMY at Évora, where 3 number of clusters cases are highlighted: 15 days (blue), 18 days (green) and 22 days (orange). These cases represent the maximum value of the gap functions in 5-clusters intervals (10-15 clusters; 15-20 clusters; 20-25 clusters), and they are candidates to be the optimal number of clusters to represent the TMY.

Fig. 1: Gap statistics for day selection

In the analysis carried out, the medoid of each cluster is selected as the most representative days, and also each of the 365 days of the TMY are assigned to one of these clusters. Table 2 shows the 18 selected days selected for representing the TMY at the site (this is expected to be the optimal case, as it reaches the highest Gap value), their DNI value and the number of days represented. This table also shows the maximal and average dissimilarity (max_diss and av_diss, respectively) between the observations in the cluster and the cluster's medoid, as well the isolation of the clusters: the maximal dissimilarity between the observations in the cluster and the cluster's medoid, divided by the minimal dissimilarity between the cluster's medoid and the medoid of any other cluster. In fig. 2 it is plotted the selected days, representing its own typical DNI value varying along a 24h period.

Clusters are numbered from 1 to 18, and also color-coded. As expected in a Mediterranean climate, most days of summer are represented by clusters 14-18 (characterized by high DNI values as well as long days), and most of winter days are represented by clusters 1-5 (characterized by shorter days and higher DNI variability). This variability across the year can be observed in fig. 3 where which of the 18 typical days are represented throughout the whole year.

From fig. 3, it is clear that from November to February the representation is mainly obtained with clusters 1 to 6, while March, April and October are transition months with clusters 7 to 12 representing most of the period. The comparison of the annual energy yield provided by the days selected, multiplied by the number of days represented by each one of the cluster days, has been compared with the solar energy yield of the 365 days of the TMY, and their differences are shown in fig. 4 as a function of the number of clusters selected (from 10 to 183 days). These differences tend to decerase at increasing number of days selected, as expected. Very low differences (<1%) are found even for the selection of few days (15 or less).

Peaks are found in almost the whole range analyzed, as expected as a trend, the amplitude decays with an increasing number of days. Even if a univocal relation between Gap function and accuracy of annual energy yield cannot be fully established, it has been found a more clear correlation by grouping clusters into intervals. Table 3 shows the optimal number of days selected as a function of the maximum number of days allowed in the cluster analysis, in 5-days intervals. It is shown the difference between TMY and days-selected electric yield, as a function of the maximum number of clusters allowed, showing a clear correlation between Gap function and accuracy in yield estimation. Difference between electric yield production using TMY data and using cluster selected days 1,1% 0,2% 0,8%

Conclusions

The methodology presented in this work allows a very significant reduction in the computational effort related to the calculation of a STE plant energy yield by simulating a reduced number of days from a high frequency TMY (90% of computing time can be reduced if 18 days are selected for representing the TMY). These days are the medoids of clusters selected according to gap statistic.

The energy yield produced by these selected days facilitates a fast and accurate, evaluation of the annual energy production of a STE plant. Concurrently, in the optimization phase of a solar plant design, many more configurations can be explored using these 18 days than using the whole TMY production analysis (with the same computing cost / time).

The computational effort of this evaluation depends on the uncertainty allowed: a tradeoff between inaccuracy (which is given at low numbers of clusters selected) and computational effort (which is given at low numbers of clusters) must be carried out in each specific analysis as it was shown for the specific location of Evora, Portugal where a STE research facility has been built, the EMSP (Evora Molten Salt Platform).

Fig. 2 :

 2 Fig. 2: left, days selected representative of the 18 clusters calculated for the TMY at Évora

Fig. 3 :

 3 Fig. 3: Days throughout the year (January to December) represented by the selected days (#18 days)

Fig. 4 :

 4 Fig. 4: Difference between annual energy yield calculated with clusters and TMY, as a function of the number of clusters selected

. 1: Radiometric station selected for this study.

	Location	Coordinates	Altitude	Pyrheliometer	Period	Climate (Köppen
	(Country)	(º)	(m)			classification)
	Évora (Portugal)	38.567 N 7.911 W	290	Kipp&Zonen CHP1	2003-2015	Mediterranean (Csa)

Tab. 2: Cluster parameters for the TMY representation

	103	10.34	16	3.15	1.92	0.69
	86	1.72	7	2.36	1.03	0.98
	289	6.76	23	2.91	1.65	1.13
	186	9.72	31	2.54	1.38	1.13
	287	7.22	17	2.83	1.33	1.10
	165	11.34	20	3.14	1.38	1.40
	228	4.50	14	3.36	1.97	0.67
	237	9.22	26	4.35	1.93	1.24
	Specific days selected	Daily DNI	Number of days
	of TMY (1-365)	(kWh/m 2 )	represented	max_diss	av_diss	Isolation
	301	1.55	23	2.60	1.56	0.98
	2	2.97	28	2.45	1.31	0.93
	328	6.23	25	4.00	1.45	1.76
	17	4.71	20	6.34	1.88	1.64
	8	0.97	15	2.38	1.21	0.68
	326	5.81	28	2.64	1.17	1.16
	276	3.88	20	2.84	1.54	1.18
	60	7.89	19	2.98	1.56	1.09
	282	2.46	11	2.70	1.96	0.76

Tab. 3: Results of cluster analysis as a function of the maximum number of clusters allowed

	Maximum number of days allowed for the cluster	15	20	25
	Optimal number of days selected	15	18	22
	Gap function value	0.2959222	0.2996370	0.2949644

© 2016. The Authors. Published by International Solar Energy Society Selection and/or peer review under responsibility of Scientific Committee doi:10.18086/eurosun.2016.09.03 Available at http://proceedings.ises.org

Acknowledgments

The authors would like to thank to ICT-Uni.Evora (Prof. Paulo Canhoto and Prof. Heitor Reis) for enabling the usage of solar radiation collected data, to project DNI approved by IPES (Portuguese Solar Energy Institute), as well as to the H2020 Program which funded Project PreFlexMS, the trigger for the study presented.