Carole Adam
email: carole.adam.rmit@gmail.com

Andreas Herzig

Dominique Longin

Vincent Louis

Unifying the intentional and institutional semantics of speech acts

Introduction

Designing efficient Agent Communication Languages (ACL) is an essential issue in Multi-Agent Systems in order to standardise exchanges between the agents. Research about the semantics of ACL sees the subscribers of the social approach [START_REF] Fornara | A commitment-based approach to agent communication[END_REF][START_REF] Chaib-Draa | Diagal : An agent communication language based on dialogues games and sustained by social commitments[END_REF][START_REF] Singh | A social semantics for agent communication languages[END_REF] criticize mentalist approaches [START_REF] Sadek | A study in the logic of intention[END_REF][START_REF] Finin | KQML as an agent communication language[END_REF] for only grounding on the agents' private mental attitudes. But one can similarly reproach to social approaches to provide a semantics only based on the agents' public commitments, independently of their mental attitudes. Now these "social attitudes" are mainly descriptive, while mental attitudes allow one to predict the agents' behaviour. Moreover mental attitudes allow agents to reason about social notions. It is thus essential to consider both mental and social attitudes. Some researchers thus propose a mixed approach based both on public and private aspects [START_REF] Gaudou | A new semantics for the fipa agent communication language based on social attitudes[END_REF]. But they do not formalise institutional speech acts like declarations. Now such speech acts are essential in new application fields involving communication about norms, roles or powers of agents, for instance in electronic commerce or automated business to business exchanges.

In this paper we thus want to propose an alternative to the well-known standard FIPA-ACL [START_REF]The foundation for intelligent physical agents[END_REF] through the following changes: relaxed feasibility preconditions to allow a more flexible utilisation of the speech acts in various contexts; new institutional speech acts like declarations and promises; an institutional interpretation of speech acts coupled with their classical intentional interpretation. Therefore we adapt an existing logical framework for the formalisation of institutional notions like roles, powers and norms [START_REF] Demolombe | Norms, institutional power and roles: towards a logical framework[END_REF]. We then formalise in this logical framework the institutional interpretation of some specific communicative actions, each one representing one of Searle's categories of speech acts (except expressive ones) [START_REF] Searle | Speech acts : An essay in the philosophy of language[END_REF]. Our notion of institution is very large: it is a set of rules and facts adopted by a group of agents, like the rules of a game, or the laws of a country; it covers formal, legal institutions as well as informal ones (e.g. social rules in a group...).

The paper is structured as follow. Section 2 discusses some other social semantics of speech acts. Section 3 briefly describes the syntax, semantics and axiomatics of our logical framework. The core of the paper (Section 4) is dedicated to the unified semantics of speech acts. We are then able to compare our semantics of ACL with some related ones in more details (Section 5). Finally we conclude about the future prospects opened by this work (Section 6).

State of the art

The mentalist approach consists in grounding the semantics of speech acts on the agents' internal mental attitudes. These are represented by belief, desire and intention modalities provided by BDI logics, that are classically used to formalise the reasoning of autonomous agents [START_REF] Rao | Modeling rational agents within a BDI-architecture[END_REF][START_REF] Wooldridge | Reasoning about rational agents[END_REF]. This resulted in the design of several standards of agent communication languages like KQML [START_REF] Finin | KQML as an agent communication language[END_REF] or FIPA [START_REF]The foundation for intelligent physical agents[END_REF], this latter one grounding on Sadek's rational interaction theory [START_REF] Sadek | A study in the logic of intention[END_REF].

These approaches were criticised a lot for being only based on private concepts (mental attitudes) instead of public verifiable notions (like commitments). Therefore some work exist aiming at enriching BDI logics with deontic operators like obligation [START_REF] Dignum | Towards socially sophisticated bdi agents[END_REF][START_REF] Broersen | Beliefs, obligations, intentions, and desires as components in an agent architecture[END_REF] or with institutional operators like count as or institutional power [START_REF] Jones | A formal characterisation of institutionalised power[END_REF], in order to formalise the institutional interpretation of speech acts exchanged by the agents. In previous work we used such an extended BDI framework to express the semantics of speech acts with institutional effects [START_REF] Demolombe | Speech acts with institutional effects in agent societies[END_REF] but we were limited to declarative speech acts, and the intentional and institutional dimensions were quite blended.

Various other work aim at providing an institutional semantics for speech acts. For example Dignum and Weigand [START_REF] Dignum | Communication and deontic logic[END_REF] propose a logical framework combining illocutionary and deontic logic to study and model the norms resulting from communication between agents; however, they only consider directive speech acts. Boella et al. [START_REF] Boella | Role-based semantics for agent communication: embedding of the 'mental attitudes' and 'social commitments' semantics[END_REF] propose a role-based semantics allowing them to combine social commitments and mental attitudes to express the semantics of speech acts in the context of persuasion dialogues. Actually they rewrite the FIPA feasibility precondition and rational effects of speech acts but replace the private mental attitudes involved by public mental attitudes attributed to the agents' roles instead of the individual agents. This solves the flaw of mentalist approaches, criticised for grounding on unverifiable mental attitudes, but finally there is no distinct institutional interpretation of speech acts, that could differ from one institution to another. In the following subsections we give some details about two approaches: Fornara and Colombetti's approach based on the notion of commitments, and Lorini et al. 's approach based on the notion of acceptance.

Fornara and Colombetti: semantics in terms of social commitments

As opposed to the mentalist approach, the social one [START_REF] Singh | An ontology for commitments in multiagent systems: Towards a unification of normative concepts[END_REF][START_REF] Singh | A social semantics for agent communication languages[END_REF][START_REF] Chaib-Draa | Diagal : An agent communication language based on dialogues games and sustained by social commitments[END_REF] assumes that private mental attitudes are not verifiable and thus grounds on the concept of public (thus verifiable) commitments [START_REF] Castelfranchi | Commitments : From individual intentions to groups and organizations[END_REF] to express the semantics of speech acts.

All the commitments taken by the agents are stored for possible future reference. The semantics of speech acts is expressed only in terms of such commitments. For example Fornara and Colombetti [START_REF] Fornara | A commitment-based approach to agent communication[END_REF] ground on Castelfranchi's notion of commitment [START_REF] Castelfranchi | Commitments : From individual intentions to groups and organizations[END_REF] to define a library of communicative acts. From the classification of speech acts into four categories (assertives, directives, commissives and declaratives) inspired from Searle's work [START_REF] Searle | Speech acts : An essay in the philosophy of language[END_REF], they redefine for each category the semantics of its speech acts in terms of social commitments. Thanks to this library, they provide a communication tool based on social commitments, alternative to the FIPA-ACL standard. This tool allows rational agents to reason about the underlying rules of communication and to respect them in order for the system to behave well.

However these authors are limited to the institutional dimension of speech acts and neglect their relations with the agents' mental attitudes. Yet agents must be able to reason autonomously about the institution before making their decision to perform a given speech act. Moreover no specific institution is explicit in their commitments, making it impossible to have different commitments in different institutions; therefore it is also impossible for speech acts to have different effects depending on the institution within which they are interpreted. For example the action of nodding one's head is interpreted in the context of French gestural language as meaning "yes", while in the context of Bulgarian gestural language it is interpreted as meaning "no". In this example the considered institutions are the respective sets of communicative rules in these two cultures.

Lorini et al. : semantics in terms of group acceptance

Lorini et al. [START_REF] Lorini | The institutional dimension of speech acts: a logical approach based on the concept of acceptance[END_REF] define a new semantics for speech acts using Gaudou et al. 's Acceptance Logic [START_REF] Gaudou | Anchoring institutions in agents' attitudes: towards a logical framework for autonomous multi-agent systems[END_REF]. A L is a modal logic extended with the notion of acceptance, representing what a group of agents willingly accept to consider as true (even if some (or all) members of the group believe the opposite) in a given institutional context (and that they can refuse in another context). Acceptances in an institutional context influence the agents' behaviour and utterances in this context. They are represented with the operator [C : x ]ϕ reading "agents in group C accept that ϕ while functioning as members of this group in the institutional context x".

Institutional notions are not primitive but defined from this notion of acceptance. Thereby a fact is an institutional fact (that it, a fact that is only valid in an institutional context, but not objectively valid) if and only if, for every non-empty set of agents, the agents in this set accept this fact as true while functioning as group members in this institutional context. In the context of ACLs, this may be a particular rule of the specific Ordinary Communication institution that these authors consider.

The authors then consider the speech act Promise in the institutional context of Ordinary Communication (OC). According to them, if i informs j that he is going to perform action α for him, and j intends i to perform this action for him, this counts as a promise at the next instant. The consequence of this promise is that i is obliged to perform action α for j. Moreover the acceptance by these two agents i and j while functioning as a group in institution OC that i has promised to perform action α for j and that j intends him to do so implies a social commitment of i towards j to perform α for him. This framework is interesting but Lorini et al. have only formalised the promise yet. Moreover they do not seem to make a clear distinction between the intentional and institutional preconditions to perform a speech act.

Our logical framework

We adapt here an existing logical framework for norms, institutional powers and roles defined in [START_REF] Demolombe | Norms, institutional power and roles: towards a logical framework[END_REF]. It is a multi-modal logic with modal operators of belief, intention, obligation, institutional facts and consequences, and action.

Syntax

Let AGT = {i, j, ...} be a finite set of agents. Let ACT = {α, β...} be the set of actions. We suppose that some actions in ACT are of the form i:α, where i is the author of action α (the agent who performs it). Let AT M = {p, q, ...} be the set of atomic formulas. Let IN ST = {s, t, ...} be the set of institutions. Complex formulas are denoted by ϕ, ψ... The language of our logic is defined by the following BNF grammar:

ϕ ::= p|¬ϕ|ϕ ∨ ϕ|B i ϕ|Ch i ϕ|I i ϕ|D s ϕ|ϕ ⇒ s ϕ|Oϕ|before α ϕ|after α ϕ
where p ranges over AT M , α over ACT , i over AGT , and s over IN ST . The classical boolean connectives ∧, →, ↔, (tautology) and ⊥ (contradiction) are defined from ∨ and ¬ in the usual manner. The operators done α ϕ, happens α ϕ, P ϕ, F ϕ and power (i , s, ϕ, α, ψ) will be defined as abbreviations.

Semantics and axiomatics

We only give here the informal meanings of our operators. It is sufficient to know that they have a Kripke semantics in terms of possible worlds. We also give some useful axioms. This framework is adapted from Demolombe and Louis' logic of norms, roles and institutional powers [START_REF] Demolombe | Norms, institutional power and roles: towards a logical framework[END_REF]. But please notice that actually, the details of the semantics of operators is not important, and any other institutional logic would work.

Belief, intention and action B i p means that agent i believes that p. Ch i p means that agent i prefers p to be true. These two normal operators have a standard KD45 axiomatics. I i p means that agent i intends that p. I i are operators defined in a KD normal modal logic. Their axiomatics is that defined for FIPA by Sadek [START_REF] Sadek | A study in the logic of intention[END_REF]. In particular intention is linked with belief by the following mix axioms:

introspection: I i p ↔ B i I i p automatic dropping of achieved intentions: I i p → ¬B i p before α and after α are normal modal operators defined in standard tense logic in linear time version [START_REF] Burgess | Handbook of philosophical logic, volume 7, chapter Basic tense logic[END_REF]. done α ϕ = ¬before α ¬ϕ means that action α has just been performed, and ϕ was true before. happens α ϕ = ¬after α ¬ϕ means that action α is about to be performed and ϕ will be true just after.

Institutional modalities Finally this framework also provides some specific operators to formalise institutional concepts. These operators have a parameter s specifying the institution within which they are valid. Here we consider an institution as a set of institutional facts and rules that a group of agents (the "members" of this institution) adopt. This is a general view that can account for various institutional contexts, be they formal institutions or informal ones: the law of a country, a contract between two parties in a business relationship, a social structure, the rules of a game... An institutional fact is a fact that is recognised to be valid in the context of a given institution, but that can make no sense in itself; i.e. it is not a physically observable fact (what Searle calls a "brute fact") but something written in the registry of this institution. For example the fact that two people are married, or that one is authorised to drive a truck, is only valid w.r.t. the law of a country; all deontic facts should also be encapsulated in an institutional fact to make the institution in which they hold explicit. We represent these institutional facts with the operator D s ϕ meaning that for institution s, it is officially established that ϕ holds. In particular if ϕ is an agent's mental attitude, then D s ϕ can be understood as this agent's commitment (either a propositional commitment if ϕ is a belief, or a commitment in action if ϕ is an intention). For instance, D FrenchLaw votingAgeis18 means that following the French law, voting age is reached at 18 years; D EU euroOfficialMoney means that in the European Union, the official money is Euro.

Institutional facts can be deduced from other facts thanks to the rules of the institution. For example the presentation of an invoice by a provider to his client counts as an obligation for the client to pay it. The existence of the invoice is physically observable, while the obligation is only valid in an institutional context. We represent these normative consequences with the primitive operator p ⇒ s q, meaning that according to the norms holding in institution s, p entails q. This operator is known in the literature as count as, and has been first formalised by Sergot and Jones [START_REF] Jones | A formal characterisation of institutionalised power[END_REF]. The following mix axioms explicit the link between institutional facts and normative consequences:

(ϕ ⇒ s ψ) → D s (ϕ → ψ) (SD) (ϕ ⇒ s ψ) → (ϕ → D s ϕ) (SC)
From these axioms and the properties of D s (see [10, p.8] for details) we can deduce:

(ϕ ⇒ s ψ) → (ϕ → D s ψ) (SP)
A particular case of normative consequence concerns the consequences of the performance of an official procedure. Actually some agents can have the power when performing a given procedure under some conditions to create new institutional facts. We represent these institutional powers as an abbreviation power (i , s, cond , α, ϕ) = ((done i:α ∧ cond) ⇒ s ϕ). Intuitively this means that i has the power in institution s, by performing action α and if condition cond holds, to see to it that ϕ becomes officially true in institution s. For example a mayor has the power in the law of the French Republic, by performing a declaration, and on condition that the two people agree, to marry them. Obviously these powers result from the agent's role in the institution, but this is not the focus of this paper so we will not remind how roles are formalised in the original framework (the interested reader can refer to [START_REF] Demolombe | Norms, institutional power and roles: towards a logical framework[END_REF] for details on this point).

Deontic modalities

We have a modality for impersonal obligation to be: Oϕ reads "it is obligatory that ϕ", and its axiomatic is that of the Standard Deontic Logic [START_REF] Jones | Handbook of philosophical logic, volume 8, chapter Deontic Logic and Contrary-to-duties[END_REF], that is KD. Obligations to do can be expressed as obligations to be in a state where the obliged action has been performed. Obligations are impersonal since no agent is explicitly responsible for their fulfilment, but such an agent can implicitly appear in their content. For instance Odone i:α means that it is obligatory (for no one in particular) to be in a state where i has just performed action α; this can be understood as "i has the obligation to perform action α".

Permissions and interdiction are defined from obligations in a standard way: P ϕ = ¬O¬p means that it is permitted that ϕ, and F ϕ = O¬ϕ means that it is forbidden that ϕ.

Please notice that no institution is explicit as a parameter of this obligation modality. But such obligations will be encapsulated in institutional facts to express the institution in which they are valid. For example D s Oϕ means that "in institution s, it is obligatory that ϕ".

Preliminary remarks

Intentional and institutional dimensions The FIPA-ACL standard [START_REF]The foundation for intelligent physical agents[END_REF] defines features allowing one to give an intentional dimension to the observation and interpretation of a communicative action: the feasibility precondition (the appropriate mental attitudes to perform the speech act) and the rational effect (this is a formula ϕ representing the content of the speaker i's intention that he intends the receiver j to know; so the performance of the speech act allows any observer k to deduce this corresponding intentional effect: B k I i B j I i ϕ). Please notice that, following [START_REF] Sadek | A study in the logic of intention[END_REF], the performance of the speech act does not automatically allow one to deduce its rational effect, but only its intentional effect, meaning that any agent k believes that the speaker i intends the hearer j to recognize its (i's) intention to achieve the rational effect ϕ. However, nothing ensures that i indeed achieves ϕ, his speech act may fail, for example the hearer may not obey an order, or may not believe an assertion. Thus the rational effect can only be deduced under some constraining hypotheses such as the sincerity and competence hypotheses used in FIPA.

In a similar way, we want to provide here the institutional dimension of the observation and interpretation of a communicative action relative to one or several institutions. This institutional interpretation is composed of the following features:

a permission condition that is necessary and sufficient for the speaker to be allowed to perform this speech act; a power condition that also needs to be true for the speech act to have an institutional effect; an explicit institutional effect that is obtained when the speech act is performed while permission and power conditions were true.

We will thus be able to combine the intentional and institutional dimensions of communicative actions (formalised as speech acts [START_REF] Searle | Speech acts : An essay in the philosophy of language[END_REF]), both essential to fully characterise their interpretation. Lorini et al. have also investigated such a unified approach but they have only formalised the interpretation of a promise in the context of ordinary communication; we aim at being much more generic.

In particular we formalise one speech act from each of Searle's categories of illocutionary forces, except the expressive one.

Actually we have relaxed some of the (widely criticised) strong constraints imposed by FIPA-ACL semantics on the appropriate context of performance of speech acts. Instead of imposing these conditions as strong constraints, we have moved them into the permission preconditions of the speech act. The agents are thus physically able to disobey these constraints, but it is forbidden by the interaction norms, and they may incur sanctions for such violations. For example, relaxing the sincerity hypothesis physically allows the agents to lie, but this will be interpreted by other agents as a violation of communicative norms.

Notations

In the sequel we use the following abbreviations:

-FP = feasibility preconditions -RE = rational effect -PermC = (institutional) permission condition -PowC = power condition -EE = institutional explicit effect Speech acts are actions of the form Force(sp, ad , inst, content) where sp ∈ AGT is the speaker, ad ∈ AGT is the addressee, inst ∈ IN ST is the institutional context, content is the propositional content and can be any formula of our language, and F orce ∈ {inf orm, promise, command, declare} is the illocutionary force.

Action laws We now explain how the intentional and institutional dimensions of actions interact by providing the action laws governing the performance of speech acts.

We notice that F P is a factual executability precondition, while P ermC is an ideal one. But even ideal worlds are submitted to physical world laws, i.e. P ermC is not sufficient for the action to be executable, F P also has to be true. For example a mayor has the permission to marry people by making a declaration, but the declaration must be executable; thus if he is voiceless one day, he will be unable to marry anyone.

We thus have the following executability laws. The factual executability law (F EL α ) means that an action happens iff its feasibility precondition is true and the agent chooses to perform it. The ideal executability law (IEL α ) means that ideally, an action should happen only if it is permitted.

happens α ↔ (FP (α) ∧ Ch i happens i:α ) (F EL α ) O(happens α → PermC (α)) (IEL α )
We also have the following effect laws. The rational effect law (REL α ) means that if the power precondition of an action is false, then only its rational effect can be deduced after its performance. The power effect law (P EL α ) means that if the power condition of an action is true, then both its rational and institutional effects can be deduced after its performance.

¬PowC (α) → after α RE (α) (REL α ) PowC (α) → after α (RE (α) ∧ EE (α)) (P EL α )
From these laws we can deduce the following theorems clarifying the factual executability and effects of α depending on the different combinations of its feasibility and power preconditions. If FP (α) is false then α is not executable.

¬FP (α) → after α ⊥

If i chooses to perform α when FP (α) is true but PowC (α) is false, then α is about to happen after which its rational effect will be true.

(Ch i happens i:α ∧ FP (α) ∧ ¬PowC (α)) → (happens α ∧ after α RE (α))
Finally if i chooses to perform α when both FP (α) and PowC (α) are true, then α is about to happen after which both its rational and institutional effects will be true.

(Ch i happens i:α ∧FP (α)∧PowC (α)) → (happens α ∧after α (RE (α)∧EE (α)))
Please notice that PermC (α) does not appear in these last two theorems, since it does not influence the feasibility of α. an agent can choose to perform a forbidden action. If we had specified an explicit sanction S (α) for forbidden performance in the institutional interpretation of α, then we could write the following theorem:

Ch i happens i:α ∧ FP (α) ∧ ¬PermC (α) → (happens α ∧ after α S (α))
However we did not specified such a sanction because it depends on many contextual parameters.

Assertives: inform

The assertive speech act Inform commits the speaker to the truth of a proposition. The notation inform(i , j , s, ϕ) reads "agent i informs j in institution s that ϕ is true".

Intentional interpretation As we said before we have relaxed FIPA constraints on the executability of speech acts. We thus impose no feasibility precondition here.

F P (inform(i , j , s, ϕ)) =

The rational effect (the content of the speaker i's intention that he intends the receiver j to know) is that j believes the promised proposition ϕ to be true:

RE(inform(i , j , s, ϕ)) = B j ϕ
Institutional interpretation The permission precondition to inform j that ϕ in institution s includes the constraints removed from the factual feasibility preconditions: the speaker should not believe that the hearer already knows if ϕ, and he should not be already committed on ¬ϕ in the same institution.

PermC (inform(i , j , s, ϕ)) = ¬D s B i Bif j ϕ ∧ ¬D s B i ¬ϕ
Now the institutional effect of Inform is to retract possible opposite commitments contracted before and to assert a new commitment on ϕ. Indeed, even if agent i was previously committed on ¬ϕ (and therefore was not permitted to inform anyone that ϕ), he may violate that obligation. But these two commitments are inconsistent so the previous one must be retracted while asserting the new contradictory one. Though one can still detect that the opposite commitment was true when i performed the action and that he has thus violated the rules of the institution. Actually due to the seriality of D s we have that D s B i ϕ → ¬D s B i ¬ϕ. So the explicit institutional effect of inform is a new institutional fact that can be interpreted as i's commitment to the truth of ϕ:

EE (inform(i , j , s, ϕ)) = D s B i ϕ
This effect is always obtained and does not depend on particular powers of i, so the power condition is trivial.

PowC (inform(i , j , s, ϕ)) =
Example For example in the context of B2B exchanges, if a provider sends his catalogue to a client, this counts as information about the prices given in this catalogue. As an effect of this action, the provider is thus committed to these prices during the validity of his catalogue. In the specific institution s constituted by the contract between the provider and the client, we assume that we have a specific rule forbidding to contradict one's commitments, which takes the form D s O(D s B i p → after α D s B i p), for every speech act α, where p is the proposition denoting that the price is 100. This means that according to the institutional contract s between i and j, it is obligatory that if an agent i is committed to believe that the price of an item is 100, then after any speech act he is still committed to this (in other words it is forbidden to retract this commitment by any speech act). From this we can deduce that the provider is obliged to respect the given prices, i.e. D s O(D s B i p → after Inf orm(i,j,s,¬p) ⊥) (it is obligatory that if i is committed to p, then the action of informing agent j that ¬p is not feasible).

Please note that the provider i can set up different contracts with different clients, in particular with different prices. This is made possible by making the institution explicit in the semantics of speech acts, and thus allowing us to specify different semantics in different institutions.

Commissives: promise to

This commissive speech act commits the speaker on a course of action. The notation promise-to(i , j , s, α) reads "i promises to j in institution s to perform action α".

Intentional interpretation

We begin with specifying the intentional dimension of this speech act, that is not given in FIPA-ACL. A promise-to is feasible if the speaker believes that the hearer intends the concerned action to be performed 3 . For example it makes no sense that a child promises to his father to play (this is rather an assertive), while it makes sense to promise him to make his schoolwork. So:

F P (promise-to(i , j , s, α)) = B i I j done α
The rational effect pursued by the speaker is that the hearer be aware of his intention to perform the promised action:

RE(promise-to(i , j , s, α)) = B j I i done i:α
Institutional interpretation In an institutional context s, this promise to perform an action α is permitted on condition that the action i :α is not explicitly forbidden itself, and that the speaker is not committed to an opposite course of action. So the permission precondition is the following:

PermC (promise-to(i , j , s, α)) = ¬D s O¬happens i:α ∧ ¬D s I i ¬done i:α
The institutional effect consists in ratifying in institution s the speaker's intention to perform action α; so after promise-to(i , j , s, α) the speaker has stored in the registry of s its intention to perform α, which is similar to him being committed in s to this course of action. EE (promise-to(i , j , s, α)) = D s I i done i:α This is thus similar to the inform(i , j , s, ϕ) speech act except that a promise stores a commitment in action while an inform stores a propositional commitment.

There is no power precondition, so the institutional effect of a (permitted) promise is always reached.

PowC (promise-to(i , j , s, α)) = Example A client c promises to pay his provider p once the ordered goods have been delivered. The action to pay is denoted by α pay This promise is valid in the context of a B2B exchange contract, that is a particular institution denoted b2b here. So this promise is formalised as: promise(c, p, b2b, α pay ). This promise is permitted since obviously the promised action to pay is not forbidden (¬D b2b O¬happens c:αpay ) and the client is not committed not to pay (¬D b2b I c ¬done c:αpay ). So when the client receives the delivery, his promise allows to deduce his commitment (or ratified intention) to pay: D b2b I c done c:αpay , that is the institutional effect of this speech act.

Directives: command

This directive speech act is commonly used by the speaker to make the hearer perform some action. The notation command (i , j , s, α, cond ) reads "i orders to j in institution s, in virtue of condition cond, to perform action α".

Intentional interpretation According to the FIPA-ACL semantics, a request is feasible only if the speaker does not believe the hearer to already intend to perform the commanded action, and does believe that the part of the feasibility preconditions of the commanded action that concerns him (i.e. that are his mental attitudes) are valid. Here we consider that when α is an action of agent j then FP (α) is of the form FP i (α) ∧ FP =i (α) where the former is "i's part of FP (α)" (similar to FIPA-ACL notation FP (α) [i\j], that is the part of FP (α) that are mental attitudes of agent i). But we do not impose this latter constraint on the feasibility of α as a feasibility precondition of the command. So:

FP (command (i , j , s, α, cond )) = ¬B i I j done j :α
The rational effect of a command (i.e. the effect that i intends j to believe that i intends to achieve) is that j has performed the commanded action:

RE (command (i , j , s, α, cond )) = done j :α

Institutional interpretation

The permission precondition to command someone to perform an action is to be empowered to do so, i.e. to dispose of the institutional power to create the obligation to perform the commanded action by commanding it under some condition cond given as an explicit attribute of the command. 4An additional permission precondition is the constraint coming from FIPA feasibility precondition that we relaxed, that is that the part of the feasibility preconditions of α that depends on i hold (one should not command someone to perform an action whose preconditions are made false by his own mental attitudes). Finally, one is not permitted to command someone to perform a forbidden action.

PermC (command (i , j , s, α, cond )) = ¬D s O¬happens j :α ∧ power (i , s, cond , command (i , j , s, α, cond ), Odone j :α ) ∧ FP i (α)
The explicit institutional effect of this power is to create two new institutional facts, corresponding to the obligation for j to perform α, and the recording of j's knowledge of his obligation. Actually this obligation could exist before, and in this case the command corresponds to a notification; but it can also be created from scratch by the command (see the examples in the next paragraph for clarification).

EE (command (i , j , s, α, cond )) = D s Odone j :α ∧ D s B j Odone j :α
This explicit institutional effect is only deduced if the power applies in the current context, i.e. if its condition is true. So:

PowC (command (i , j , s, α, cond )) = cond
Example For example a parent can command his children to clean his room. In this case, the action becomes obligatory through the command, because of the parent's authority over his son. In other words, his parent role gives him the institutional power to command his child to perform actions, under some conditions on the nature of the actions. Similarly a professor commanding his students to make some schoolwork creates the obligation for them to do so, on the strength of his role of professor. Indeed the role of professor gives an institutional power to command students to perform schoolwork, under the condition that it is related to the course.

But an order does not necessarily create an obligation, and may just put in focus an existing one. For example a bailiff can be sent to officially command an uncooperative client to pay an invoice. In this case the obligation already exists (and is attested by the invoice) so the bailiff only reminds the client of it 5 . He is permitted to perform such a command in virtue of his role of bailiff (which gives him the power to force clients to pay) and because he is sent by the provider (which constitutes the applicability condition of this power).

Declaratives: declare

This declarative speech act changes the institutional reality by creating a new institutional fact. The notation declare(i , j , s, cond , ϕ) reads "i declares to j in institution s that given condition cond, the fact ϕ is now established". The condition usually bears upon the speaker's role that empowers him to perform such a declaration.

Intentional interpretation This intentional interpretation is partly inspired from the intentional interpretation of an inform(i , j , s, D s ϕ). The feasibility precondition of a declaration is that the speaker does not believe the declared fact to be already established (indeed a declaration must create a new institutional fact). The rational effect (i.e. the intended effect) has two parts: the first one is to make the declared institutional fact true; the second part is similar to the rational effect of an inform about D s ϕ, i.e. to make the hearer aware of this information. So:

FP (declare(i , j , s, cond , ϕ)) = ¬B i D s ϕ RE (declare(i , j , s, cond , ϕ)) = B j D s ϕ ∧ D s ϕ
Institutional interpretation The permission precondition to perform declare(i , j , s, cond , ϕ) is that i really has the power to establish the declared fact ϕ by declaring it under the announced conditions cond. This power is locally granted by each specific institution to some agents depending on their role. For example the French republic grants the mayors the right to pronounce two people husband and wife, under the condition that they both consent to it. Thus an ordinary agent who is not mayor does not have this power, so that he is not allowed to pronounce marriages.

PermC (declare(i , j , s, cond , ϕ)) = power (i , s, cond , declare(i , j , s, cond , ϕ), ϕ)

The explicit effect of a declaration is to store the declared fact in the institution, as well as the fact that the hearer is officially aware of this fact.

EE (declare(i , j , s, cond , ϕ)) = D s ϕ ∧ D s B j D s ϕ
This explicit effect is only obtained under the additional condition that cond is valid:

PowC (declare(i , j , s, cond , ϕ)) = cond

Example For example a country can declare war to another one, by the voice of its representative that is empowered to do so, and under some conditions like the agreement of some counsellors. A mayor is empowered by its country to pronounce weddings under some conditions that the people are of age and consenting.

Citizens have to declare their income to the public treasury in order to calculate the amount of tax that they will pay. This is a declaration since the effect is a new institutional fact officially establishing one's declared income as being believed by him. Any citizen is empowered to do so. Moreover the law imposes a constraint on the generated commitment, that is an obligation to believe this income to be true. Thereby if the declared income was false the citizen is liable for prosecution and sanctions.

Example of reasoning with our action laws

This example is situated in the context of a B2B exchange (in institution b2b) between a buyer b and a seller s. The seller intends potential clients to know the prices of his products, e.g. I s B b p. With our relaxed feasibility precondition, he can use an assertive speech act whatever the context. Though if the buyer has already been informed of the prices before (D b2b B s B b p), the seller is not permitted to inform him again. Thus if he informs him anyway, according to IEL α he violates an obligation. This can be detected by other agents, and specific rules of the institution may specify sanctions to compensate this. Being aware of such pre-specified sanctions, an agent can deliberately choose to violate an obligation if the intended outcome (here, that clients be aware of the seller's offer) is more important than the incurred sanction. This shows the importance of having both intentional and institutional semantics of speech acts, to allow agents to reason about the relative importance of their goals and their obligations, in order to make an appropriate decision.

Detailed comparison with other work

In this section we compare our semantics of speech acts with those proposed by Fornara and Colombetti, and by Lorini et al. (that we have presented above).

Concept of commitment

We have shown before that what we mean by commitment in this work is a ratified mental attitude, i.e. a mental attitude (belief or intention) stored in the institution. This notion is similar to Fornara and Colombetti's commitment that is also a public concept, except that we have not made explicit its creditor. Actually the debtor is committed towards the whole institution, but an implicit creditor can sometimes be found in the content ϕ of the commitment. For example if agent i promises to j to pay him, he commits himself to a proposition involving agent j, expressing that j will be payed at some future instant. The creditor can sometimes be found in the sanction associated with the violation of the commitment, too; for example the obligation to pay damages to an agent.

Our notion of ratified mental attitude is also similar to Gaudou et al. 's notion of acceptance, because it must influence the agent's behaviour and utterances. Indeed, the agent's ratified mental attitudes are mental attitudes that he has expressed, that are stored in the institution, and to which he must conform while subsequently acting and speaking, even if they are not consistent with his real mental attitudes. For example an agent who promises that he has seen a given movie must then be able to talk about it in order to be consistent with his promise; if he is unable to narrate the end of the movie one can notice that he is contradicting his commitment.

Notion of institution

By institution we mean a set of rules and facts that are adopted by a group of agents (the members of the institution). This seems to be a more generic notion than Lorini et al. 's concept of informal institution, since it accounts for this particular kind of institutions but also for various other ones: laws of a country, rules of a game, contract between businesses, social norms of a culture... In particular it allows to have institutional rules that are ignored by the members of the institution, what is the case for law for example, since one cannot be aware of the whole set of laws of his country, while he is one of its citizens. Fornara and Colombetti do not make explicit the institutional context in which their speech acts are interpreted, so we believe that they also consider a kind of "ordinary communication" institutional context.

In our view informal institutions are described by a specific set of facts and rules, determining their specific functioning. In particular the fact that all agents must accept a fact for it to become institutional is a particular institutional law. In other kinds of institutions, facts must be adopted by a majority of members (voting to create a law or to elect the president for example), or the opinion of one single member can suffice (the referee is always right). Thus we cannot adopt such an hypothesis in our account. Indeed on the contrary we consider the generic interpretation of speech acts in any institution s. More specific rules can be additionally specified in each particular interpretation, but the object of this paper is to identify for each category of speech acts the features that are common to their institutional interpretations whatever the institutional context.

Conclusion

In this work we have provided an expressive logical framework blending the agents' mental attitudes (beliefs, intentions) with their social attitudes (obligations, institutional facts and powers...). To illustrate its expressivity, please notice that our framework allows to represent some forms of contrary-to-duty obligations-to-do. Such obligations take the form:

Oafter α ⊥ → after α Odone repairα where repair α is the contrary-to-duty obligation associated to the violation of the obligation to refrain from doing α. This means that if it is forbidden to perform α, then after α it is obligatory to perform a repairing action repair α .

We have then used this framework to provide a semantics for an agent communication language based on FIPA-ACL but relaxing its widely criticised too constraining feasibility conditions, and adding permission preconditions. This way, agents can choose to perform forbidden speech acts but would then be liable to sanctions in the corresponding institution. Our ACL semantics also includes new speech acts (commissives and declaratives). It generalises existing approaches by unifying the intentional and institutional dimensions in one single framework, while strongly distinguishing them; moreover it allows to consider various kinds of institutional contexts; finally it provides action laws taking both dimensions into account.

In future work we intend to improve the institutional and intentional semantics of speech acts by accounting for deadlines. Various researchers [START_REF] Broersen | Designing a deontic logic of deadlines[END_REF][START_REF] Dignum | Obligations and dense time for specifying deadlines[END_REF][START_REF] Demolombe | Norms with deadlines in dynamic deontic logic[END_REF] have shown that an important feature of obligations to perform an action is the deadline before which this action must be performed, that is essential to be able to assess the violation or fulfillment of such obligations. Though for the sake of simplicity we have omitted deadlines in this paper. An idea to manage them in future work could be to use existing formalisations of norms with deadlines, or to ground on linear temporal logic with until and since operators [START_REF] Burgess | Logic and time[END_REF].

Finally we would like to mention that our framework for the institutional interpretation of speech acts has been successfully implemented into institutional agents that have been used in a prototype of industrial application: a multi-agent mediation platform for automated business to business exchanges [START_REF] Bourge | A multi-agent mediation platform for automatic b2b exchanges[END_REF].

Please notice that threats such as "I promise that I will kill you" cannot be considered as promises in the sense of Searle.

Institutional powers obviously depend on roles. This notion has been explored in previous work[START_REF] Demolombe | Norms, institutional power and roles: towards a logical framework[END_REF] but we will not enter in the details here since they are not in the scope of this paper.

Actually this seems to be a notification rather than a command, but the aim is to make the client behave, while the aim of a notification is only to make the receiver officially aware of what is notified. In further work we expect to study into more details the links between declarations, commands and notifications.


Ronglin Tang

Zhao-Liang Li
email: lizhaoliang@caas.cn

Estimating daily evapotranspiration from remotely sensed instantaneous observations with simplified derivations of a theoretical model

Keywords: Evapotranspiration, Remote sensing data, Constant evaporative fraction method



Five methods are developed for converting remotely sensed instantaneous ET to daily values



The applicability and robustness of the five methods are evaluated using ground-based eddy covariance measurements and MODIS-based estimates



The constant  method, the constant Rc method, and the constant Rc/Ra method could produce daily ET estimates with a reasonable accuracy

Introduction

Evapotranspiration (ET, water in mm/d, equivalent to latent heat flux) is one of the key components in global hydrological cycle and energy budget on the earth. Continuous efforts have been made over the past decades to develop models with varying degree of structure complexities and uncertainties for estimating land surface ET with remote sensed data [START_REF] Li | A Review of current methodologies for regional evapotranspiration estimation from remotely sensed data[END_REF][START_REF] Kalma | Estimating land surface evaporation: a review of methods using remotely sensed surface temperature data[END_REF]. Nonetheless, most models only provide instantaneous snapshots of surface ET at the satellite overpass times. To improve the practical applicability of the remotely sensed ET, researchers have always been seeking for a temporally stable ratio of ET to a physical variable that can be applied to effectively convert the instantaneous ET to daily values and a number of methods with different level of accuracies are developed under such context [START_REF] Brutsaert | Application of self-preservation in the diurnal evolution of the surface energy budget to determine daily evaporation[END_REF][START_REF] Trezza | Evapotranspiration using a satellite-based surface energy balance with standardized ground control[END_REF][START_REF] Ryu | On the temporal upscaling of evapotranspiration from instantaneous remote sensing measurements to 8-day mean daily-sums[END_REF]Tang & Li, 2017].

One of the most representative schemes is the well-known constant evaporative fraction (EF, defined as the ratio of ET to surface available energy) method. This method, which simply assumes that the instantaneous EF equals the daily average, is perhaps the most widely used scheme for the conversion of instantaneous ET to daily values. However, due to the concave-up shape of the daytime EF on clear-sky or constant-cloud days, many authors have reported that the constant EF method tends to significantly underestimate the daily ET [START_REF] Tang | Verification of land surface evapotranspiration estimation from remote sensing spatial contextual information[END_REF][Tang et al., , 2013a;;Tang & Li, 2017;Van Niel et al., 2011;[START_REF] Cammalleri | Applications of a remote sensing-based two-source energy balance algorithm for mapping surface fluxes without in situ air temperature observations[END_REF][START_REF] Delogu | Reconstruction of temporal variations of evapotranspiration using instantaneous estimates at the time of satellite overpass[END_REF][START_REF] Xu | Temporal upscaling and reconstruction of thermal remotely sensed instantaneous evapotranspiration[END_REF][START_REF] Chávez | Daily evapotranspiration estimates from extrapolating instantaneous airborne remote sensing ET values[END_REF] and the underestimation can even reach as large as 34% [START_REF] Van Niel | Upscaling latent heat flux for thermal remote sensing studies: comparison of alternative approaches and correction of bias[END_REF]. Similar to the constant EF method that makes use of surface available energy as the conversion variable, some other schemes [START_REF] Trezza | Evapotranspiration using a satellite-based surface energy balance with standardized ground control[END_REF]Cha´vez et al., 2008;[START_REF] Ryu | On the temporal upscaling of evapotranspiration from instantaneous remote sensing measurements to 8-day mean daily-sums[END_REF][START_REF] Van Niel | Upscaling latent heat flux for thermal remote sensing studies: comparison of alternative approaches and correction of bias[END_REF]Tang et al., 2015aTang et al., , 2017] ] have also attempted to assume a temporally stable ratio of ET to surface downward solar radiation, surface net radiation, extraterrestrial solar radiation, or reference grass/alfalfa ET in a diurnal cycle. Except the constant reference EF (the ratio of actual ET to reference grass/alfalfa ET) method, which assumes the constancy of reference EF, the conversion schemes are incapable of accounting for the temporally variable environmental factors (e.g., wind speed, air humidity, air temperature, air pressure) and the horizontal advection on the ET in a diurnal cycle. Note that all these schemes have been extensively evaluated and applied for the conversion of instantaneous ET to daily values, but consistent conclusions have seldom been drawn, perhaps because each scheme has its own advantages and drawbacks and scope of application. For example, Tang et al. [2013a] comprehensively reviewed several ET conversion methods and discussed in-depth their advantages and weaknesses and found that the constant reference EF method had the best performance for the ET conversion; [START_REF] Van Niel | Upscaling latent heat flux for thermal remote sensing studies: comparison of alternative approaches and correction of bias[END_REF] concluded from results on selected days over a ~10-year period that using surface downward solar radiation as the conversion variable performed better than using extraterrestrial solar radiation and surface available energy; [START_REF] Chávez | Daily evapotranspiration estimates from extrapolating instantaneous airborne remote sensing ET values[END_REF] reported that the constant EF method complemented the constant reference EF method and the former performed better under heterogeneous vegetation cover conditions with moderate to considerable soil water stress and under non-advective climate conditions while the latter worked better under more homogeneous surface conditions with little to no plant soil water stress and under advective conditions. The objectives of this paper are twofold: 1) to develop alternative methods for the conversion of instantaneous ET to daily values, and 2) to test the applicability and robustness of the methods using ground-based eddy covariance measurements and MODIS-based estimates. To this end, a theoretical relationship between instantaneous and daily ETs is first deduced from the classical Penman-Monteith equation. Five conversion methods are then derived from the derivatives of the theoretical relationship with a certain degree of assumptions. Section 2 presents the methodology of how the five ET conversion methods are derived. Section 3 describes the study site, the ground-based meteorology and energy flux measurements, and the MODIS-based instantaneous ET datasets. Section 4 provides the results and discussion of the ET conversion. Conclusions are finally made in Section 5.

Methodology

This study is motivated by the oversimplification of the widely applied constant EF method and several other similar methods that cannot capture the diurnal variation of environment variables and as a result may produce significant biases in converting instantaneous ET to daily values. Beginning with the physics-based Penman-Monteith equation, [START_REF] Mcnaughton | Predicting effects of vegetation changes on transpiration and evaporation[END_REF] rearranged it in the following form to study the relative contribution of the radiative (LE rad ) and aerodynamic (LE aero ) terms to the overall evapotranspiration, (1 )

rad aero eq im LE LE LE LE LE       (1)
where LE is the latent heat flux, W/m 2 ; LE eq is the equilibrium evapotranspiration, W/m 2 ; LE im is the evapotranspiration imposed by the surrounding air, W/m 2 ; and  (-) is the decoupling factor representing the degree of atmosphere-vegetation interaction. With a series of computations and substitutions, Eq. ( 1) can be rewritten as follows [START_REF] Pereira | The Priestley-Taylor parameter and the decoupling factor for estimating reference evapotranspiration[END_REF]

: = = ( ) eq n LE LE R G      (2) * /     (3) 1 1 c a R R      (4) 1 1 a R R      (5) * () () p n C VPD R RG      (6)
where  is the Priestley-Taylor parameter, Δ is the slope of the saturated vapor pressure versus air temperature curve, kPa/°C; is the psychrometric constant, kPa/°C; R c is the surface resistance, s/m; R a is the aerodynamic resistance, s/m; R * is the critical surface resistance when LE equals equilibrium evapotranspiration, s/m; is the air density, kg/m 3 ; C p is the specific heat of the air, J/(kg•°C); VPD is the vapor pressure deficit of the air, kPa; R n is the surface net radiation, W/m 2 ; and G is the soil heat flux, W/m 2 .

Studies have shown that Eqs. (2-6) are valid at both instantaneous and daily time scales [START_REF] Allen | Crop evapotranspiration-Guidelines for computing crop water requirements[END_REF]ASCE-EWRI, 2005]

i d i i d d n d n i d d i i i d i i i d nd n i d d i d i LE LE R G RG LE RG RG                          (7)
Eq. ( 7) clearly depicts the physical relationship between daily LE (or EF) and instantaneous LE (or EF) with a multiplication of multiple fractions ( * *

d i i i d di d d i d i EF EF             
). There is essentially only one unknown parameter (daily R c ) in this equation if instantaneous LE is already estimated and other instantaneous and daily meteorological parameters are known.

To obtain the daily LE from instantaneous values, five conversion methods can be derived with different assumptions/simplifications made to Eq. (7) as follows,

(i) Assuming * * 1 d i i i d d d i d i              , which is equivalent to id EF EF  , called the constant EF method. (ii) Assuming * * 1 id di

  

, equivalent to id   in Eq. ( 2), called the constant  method.

(iii) Assuming

1 d i   
, called the constant  method.

(iv)

Assuming ( ) ( )

c i c d RR  , called the constant R c method. (v) Assuming ( ) ( ) cc id aa RR RR  , called the constant R c /R a method.
Methods (ii-v) can also be interpreted as a correction of method (i). Daily values of air temperature, wind speed, air vapor pressure, air pressure, and surface available energy, if demanded, are computed as the average of multiple (48 half-hourly in this study) measurements from 0:00 h to 24:00 h local time. Daily psychrometric constant and daily slope of the vapor pressure curve are estimated using daily air pressure and daily air temperature, respectively, following Eqs. ( 8) and ( 13) in [START_REF] Allen | Crop evapotranspiration-Guidelines for computing crop water requirements[END_REF]. Daily VPD is computed as daily saturated vapor pressure (estimated using daily air temperature) minus daily air vapor pressure. Aerodynamic resistance (R a ) is calculated for simplicity by assuming that the atmosphere is under neutral conditions (i.e., no stability correction function is applied).

Test site and data

3. [2011a, 2013a, 2015b] for the specifics of the sensors and the sensor deployment. In addition, an eddy covariance (EC) system, consisting of an open-path CO 2 /H 2 O gas analyzer (model LI-7500, Licor Inc., Lincoln, Nebraska) and a 3-D sonic anemometer/thermometer (model CSAT3, Campbell Scientific Inc., Logan, Utah), is setup to measure the turbulent sensible heat flux and latent heat flux. Measurements from the EC are collected by a data logger at a 10-Hz frequency for archiving and 30-min averaged fluxes are computed. Online flux computation and post-field data programs are applied to correct for the effect of the sonic virtual temperature, the time-lag, the performance of the planar fit coordinate rotation, the density fluctuation, and the frequency response [START_REF] Webb | Correction of flux measurements for density effects due to heat and water vapour transfer[END_REF][START_REF] Burba | A brief practical guide to eddy covariance flux measurements: principles and workflow examples for scientific and industrial applications[END_REF]. The eddy fluxes are quality-controlled following the work of [START_REF] Aubinet | Estimates of the annual net carbon and water exchange of European forests: The EUROFLUX methodology[END_REF] and Foken et al. [2004]. The height of the EC sensors switches from ~4.3 m above surface ground (ASG) in late July or early August to ~2.9 m ASG in mid-to late October each year.

Half-hourly measurements of surface meteorological and energy flux variables from late April 2009 to late October 2011 were collected for analysis in this study. These data were first carefully checked following the procedures proposed by Tang et al. [2013a] to ensure quality and completeness. Specifically, these procedures are 1) the removal of data spikes and abnormalities in sensible heat flux and latent heat flux measurements (< -100 W/m 2 or > 700 W/m 2 , beyond the limits of surface net radiation), 2) the exclusion of days that have data gaps (e.g., caused by rainfall, instrument malfunction or maintenance) in any of the 48 half-hourly measurements or have abs(EF) > 3 at assumed satellite overpass time and at daily scale. Moreover, because the constant r c method and the constant r c /r a method are significantly impaired under conditions of wind speed < 0.5 m/s or relative humidity = 100%, the days with such extreme weather at assumed satellite overpass times are further excluded in the analysis. The daily LE for the validation is derived by averaging the 48 half-hourly EC measurements with or without an energy imbalance correction in a diurnal cycle.

MODIS-based datasets

Three groups of reliable MODIS-based instantaneous LE and R n -G datasets, which were estimated using a typical dual-source surface energy balance model at the Yucheng station, are extracted from our previous studies for the evaluation of the five ET conversion methods. These datasets are characterized by different magnitudes of model-estimation bias and error and would be especially helpful for testing the robustness of the five ET conversion methods. Specifically, these datasets are derived using (A) the N95 [START_REF] Norman | A two-source approach for estimating soil and vegetation energy fluxes from observations of directional radiometric surface temperature[END_REF] [2011a] and Tang et al. [2013a].

The five methods for converting instantaneous ET to daily values will be evaluated and intercompared using two groups of inputs (see Figure 1), namely ( 1 and MODIS/AQUA daytime overpass times, respectively. Studies [START_REF] Twine | Correcting Eddy-Covariance Flux Underestimates over a Grassland[END_REF][START_REF] Prueger | Tower and aircraft eddy covariance measurements of water vapor, energy and carbon dioxide fluxes during SMACEX[END_REF][START_REF] Foken | The energy balance closure problem: An overview[END_REF]Tang et al., 2011bTang et al., , 2013b] ] have reported that an energy imbalance is often found between the EC-measured turbulent heat fluxes and surface available energy whereas an energy balance among the energy flux components is by definition enforced in remotely sensed surface energy balance models. This contradiction compels an energy balance correction made to the EC measurements. Since maintaining a constant Bowen ratio is physically more reasonable based on the underlying theory of eddy covariance [START_REF] Twine | Correcting Eddy-Covariance Flux Underestimates over a Grassland[END_REF] and forcing closure by applying the residual to the LE is valid only for arid and semi-arid regions where the Bowen ratio tend to be quite high [START_REF] Prueger | Tower and aircraft eddy covariance measurements of water vapor, energy and carbon dioxide fluxes during SMACEX[END_REF], evaluation of the five ET conversion methods will be conducted using EC measurements corrected by the Bowen ratio (BR) method. In addition, to determine whether the energy imbalance correction influences the consistency of the model performance, evaluation of the five ET conversion methods with the first group of inputs is also discussed using uncorrected EC measurements and using EC measurements corrected by the residual energy (RE) method [START_REF] Twine | Correcting Eddy-Covariance Flux Underestimates over a Grassland[END_REF]. The BR correction method conserves the EC-measured Bowen ratio to repartition surface available energy into sensible heat flux and LE. The RE correction method brings all of the imbalanced energy (surface available energy minus the sum of sensible heat flux and LE)

to the EC-measured LE. The ratio of the EC-measured daytime to daily LEs before and after the correction is assumed constant to derive the corrected daily LE measurement, as done in our previous studies [Tang et al., 2013a[Tang et al., , 2017] ] to overcome the weakness of the BR or RE method.

Ground

Results and discussion

Validity of the constancy assumption of the ET conversion methods

Before evaluating the five ET conversion methods (namely the constant EF method, the constant methodthe constant methodthe constant Rc method, and the constant Rc/Ra method), we first examined how the EF, , , Rc, and Rc/Ra at half-hourly scale were different from those at daily scale (i.e., the validity of the assumption of constant EF, , , Rc, and Rc/Ra). Figure 2 shows the daytime variation of the multi-day averaged EF, , , Rc, and Rc/Ra that were estimated using ground-based EC and meteorology measurements at the Yucheng station. The estimated daily values of the five variables were averaged over 374 days while the available days were different for averaging each half-hourly values.

From mid-morning (9:00 h local time) to mid-afternoon (15:00 h local time), covering the daytime overpass times of most polar-orbiting satellites, the multi-day averaged half-hourly EF, , , and Rc underestimated their daily mean whereas the half-hourly Rc/Ra overestimated its daily mean. The  at half-hourly scale relative to its daily mean had a larger underestimation than the EF and the and the  had the smallest underestimation among these three variables. The underestimation of EF, , and Rc became weaker whereas the overestimation of Rc/Ra became stronger when the conversion time varied from morning to afternoon. The half-hourly  remained relatively more stable from mid-morning to mid-afternoon than the other four variables. The half-hourly EF had a very similar non-linear variation shape to the half-hourly  while the half-hourly  varied almost inversely with the half-hourly Rc/Ra during the daytime. The Rc had a more significant change in its diurnal pattern than the other four variables. Figure 3 compares the half-hourly EF, , , Rc, and Rc/Ra estimated at 10:30 h (N=357) and 13:30 h (N=360) local time and those at daily scale. The EF and  at half-hourly scale relative to their daily mean were underestimated with large biases of -0.22 and -0.39 (relative biases of -32% and -36%) and RMSEs of 0.50 and 1.09 (relative RMSE of 73% and 99%) at 10:30 h local time and biases of -0.16 and -0.35 (relative biases of -24% and -32%) and RMSEs of 0.48 and 1.06 (relative RMSE of 69% and 95%) at 13:30 h local time, respectively. The  and Rc were underestimated with lower biases of -0.06 and -145 s/m (relative biases of -12% and -25%) and RMSEs of 0.14 and 881 s/m (relative RMSE of 29% and 151%) at 10:30 h local time and biases of -0.06 and -34 (relative biases of -13% and -6%) and RMSE of 0.16 and 973 s/m (relative RMSE of 33% and 166%) at 13:30 h local time, respectively. Overestimations of Rc/Ra were found with biases of 1.3 and 3.1 (relative biases of 23% and 53%) and RMSEs of 9.6 and 14.6 (relative RMSE of 171% and 261%) at 10:30 h and 13:30 h local time, respectively. In addition, the bias tended to be larger at high values of the five variables, especially for the EF, ,Rc, and Rc/Ra. For the  variable, there were almost no differences between the bias and RMSE at 10:30 h and those at 13:30 h; for the Rc variable, the bias at 10:30 h local time was much higher than that at 13:30 h local time while for the Rc/Ra variable opposite results were obtained; for the EF and  variables, slight differences of the bias and RMSE were found between the two conversion time.

Evaluation of the ET conversion methods using completely ground-based measurements

Figure 4 compares the daily LE estimated using the five derived conversion methods at 10:30 h and 13:30 h local time with ground-based EC measurements corrected using the BR method. Figure 5 compares the relative bias and relative RMSE in the validation of the daily LE. Several findings are summarized as follows. i) Overall, the constant Rc method and the constant  method could produce good daily LE with the lowest bias (relative bias falling in between -10% and 7%) and RMSE (relative RMSE falling in between 20% and 15%), respectively, and the two statistics were of limited variation when the conversion time was switched from 10:30 h to 13:30 h local time, whereas large underestimations in the validation of the estimated daily LE were found in the constant EF method and the constant  method, with relative biases of -22% and -25% (-17% and -23%) and relative RMSEs of 30% and 34% (25% and 31%) at 10:30 h (13:30 h) conversion time, respectively. ii) The constant EF method, the constant methodthe constant methodand the constant Rc/Ra method were all shown to underestimate the daily LE whereas the constant Rc method showed a change from an overestimation at 10:30 h to a very small underestimation at 13:30 h of the daily LE. The underestimation bias (the difference between the estimated and observed daily LE) and RMSE for the former four methods varied between -18.2 W/m 2 and -3.3 W/m 2 and between 24.4 W/m 2 and 14.5 W/m 2 at 10:30 h conversion time, respectively, and they varied between -16.5 W/m 2 and -7.1 W/m 2 and between 22.2 W/m 2 and 13.7 W/m 2 at 13:30 h conversion time, respectively. The bias and RMSE for the constant Rc method were 5.5 W/m 2 and 14.0 W/m 2 at 10:30 h conversion time, respectively, and they were -0.4 W/m 2 and 10.3 W/m 2 at 13:30 h conversion time. iii)

The constant method and the constant EF method overall produced the highest and the second highest underestimation bias and RMSE, respectively, but the underestimation of the daily LE was reduced when the conversion time was switched from 10:30 h to 13:30 h local time.

The evaluation using uncorrected EC measurements or EC measurements corrected by the RE method did not change much the better or worse performance of a given ET conversion method relative to other methods that is obtained using EC measurements corrected by the BR method, as could be seen from Figure 5. Overall, the constant  method and the constant Rc method were still among the top two schemes for producing reasonably good daily LE whereas the constant method and the constant EF method overall were still the two worst schemes. The constant Rc/Ra method had a similar performance to the constant  method at 13:30 h local time when the RE correction method was applied.

Evaluation of the ET conversion methods using MODIS-based datasets

Figures 6-7 compare the daily LE estimated from the three groups of instantaneous MODIS-based datasets using the five conversion methods with ground-based EC measurements corrected using the BR method. Figure 8 illustrates the relative bias and relative RMSE in the validation of the daily LE converted from the MODIS-based datasets. The constant EF method and the constant  method both showed an underestimation of the daily LE. They produced the relative biases of -9% ~ -12% and of -15% ~ -17% and the relative RMSEs of 20% ~ 27% and of 25% ~ 31%, respectively. The constant Rc method overestimated the daily LE by 6% ~ 18% with the relative RMSE varying between 16% and 30% for the three groups of the MODIS-based datasets. The constant method and the constant Rc/Ra method overestimated the daily LE by 4% ~ 9% and 2% ~ 7% for two (N95-derived LE datasets from Tang et al. [2011a] and MODIS/TERRA-based LE datasets from Tang et al. [2013a]) of the three groups of the MODIS-based datasets, respectively, and underestimated the daily LE by -2% and -6% for the left group of the MODIS-based datasets (MODIS/AQUA-based LE datasets from Tang et al. [2013a]). The relative RMSE varied between 13% and 28% for the constant method and between 15% ~ 29% for the constant Rc/Ra method. For each of the three groups of the MODIS-based datasets, the constant method and the constant Rc/Ra method produced smaller (at least similar) biases and RMSEs than the constant EF method and the constant  method.

Overall, the constant method and the constant Rc/Ra method performed the best and could produce reasonably good daily LE when remote sensing instantaneous LE and other inputs were provided without significant biases. The constant Rc method, which produced a similar magnitude of RMSE to the constant method and the constant Rc/Ra method but had a relatively larger bias, performed slightly worse. The constant  method performed the worst with a largest underestimation of the daily LE. The constant EF method with the second largest bias and RMSE performed slightly better than the constant  method.

Discussion and sensitivity analysis

All of the five methods proposed in this study for converting remotely sensed instantons ET to daily values are essentially reduced forms of the rearranged Penman-Monteith equation and their performance depends on how the instantaneous EF, , , Rc, and Rc/Ra differ from those at daily scale. If the assumption on each of the five ET conversion methods, as presented in Section 2, is tenable, these methods will produce daily LE estimates without any bias. If daily EF, , and  are higher than (daily Rc and Rc/Ra are lower than) their instantaneous values, the corresponding method will underestimate the daily LE, and vice versa. Results as presented in Section 4.1 clearly indicate that daily EF, , , and Rc is overall higher than instantaneous values while Rc/Ra at daily scale is lower than that at instantaneous scale in most cases. Varying degree of assumptions or simplifications make the five methods differ in model inputs, structure, and accuracy. Given the roughest assumption as presented in Section 2, the constant EF method estimates daily LE with only instantaneous EF and daily surface available energy as inputs. The constant  method, the constant method, the constant Rc/Ra method, and the constant Rc method gradually relax the assumption of the constant EF method and thus allow themselves to adjust for the relative difference between the instantaneous EF (or Rc/Ra) at the time of the satellite overpass and the EF (or Rc/Ra) during other timeframes in a more physics-based manner. The concave-up shape of the daytime EF from morning to afternoon that is reported by many studies and also shown in this study partly contributes to the underestimation of daily LE in the constant EF method. Moreover, due to the unstable EF resulting from the negative surface available energy and the very low ET in the nighttime, the constant EF method cannot effectively consider the effect of the nocturnal ET on the total daily ET. The direct relationship between the EF and the  as shown in Eq. ( 2) results in the very similar non-linear shape of daytime EF to that of daytime . Because Δ/(Δ+) increases when air temperature rises, the underestimation will further be strengthened using the constant  method compared to the constant EF method, leading to a larger underestimation of daily LE. The relationship between the  and the Rc/Ra as presented in Eq. ( 4) explains the inverse shape of daytime  and Rc/Ra. Because of the limited variability of /(Δ+), the constant method could have a similar performance to the constant Rc/Ra method under some circumstances. The significant change of daytime Rc is attributed to the wide variation of environmental variables and causes a more complex relationship between daily Rc and instantaneous Rc.

However, the constant Rc method seems to be less dependent on this complex relationship. The smaller underestimation of half-hourly EF, and Rc (the larger overestimation of half-hourly Rc/Ra) relative to the daily mean in the afternoon than in the morning indicates that using remotely sensed data acquired at afternoon overpass rather than morning overpass can produce better (worse) daily LE estimates with these three methods. Due to the more stable daytime  the constant method could produce daily LE estimates that are more independent on the satellite overpass time. Different from the constant EF method, the other four methods are capable of considering the non-linear effect of meteorological factors on the ET. In the daily ET estimates than the constant method, the constant Rc method, and the constant Rc/Ra method. Other strength of the latter three methods is their more solid physical foundation and the weakness primarily lies in the requirement of additional instantaneous and daily ground-based meteorological data (air temperature, VPD, and wind speed) and vegetation height (or surface roughness length), besides the instantaneous EF and daily surface available energy, as inputs, which may be unavailable from remote sensing data. The five methods can be applied to different ecosystems for the conversion of remotely sensed instantaneous ETs to daily values. The findings at the cropland site in this study may be extended to other ecosystems as long as the inputs (instantaneous and daily meteorological variables, remotely sensed instantaneous LE and R n -G) for each method are provided with reasonable accuracies. Note that the application of the constant Rc method or the constant Rc/Ra method firstly requires the instantaneous Rc to be inversely estimated from the Penman-Monteith equation.

To better understand the error propagation of the five methods, a sensitivity analysis adapted from the work of [START_REF] Zhan | An intercomparison study on models of sensible heat flux over partial canopy surfaces with remotely sensed surface temperature[END_REF] was made. In this sensitivity analysis, the model-estimated daily LE by converting half-hourly measurements at 13:30 h local time was used as the reference daily LE. We made a certain perturbation to each of the inputs of the five ET conversion methods and the daily LE estimates were then updated with the inputs of the perturbated variable and other unchanged variables. Results (see Table 1) showed that instantaneous LE, among other inputs, had the largest effect on all of the five methods. A perturbation of 10% in instantaneous LE on average resulted in a variation of -10% to 10% in the daily LE estimates in the constant EF method, the constant  method, and the constant  method, a slightly lower variation of -8.4% to 8.2% of the daily LE estimates in the constant Rc method, a slightly higher variation of -11.0% to 11.2% of the daily LE estimates in the constant Rc/Ra method. Because daily values of the input meteorological variables are primarily obtained using the average of the half-hourly measurements, the sensitivity of these variables may be counteracted or further enhanced. For example, A perturbation of 10% in instantaneous and daily surface available energies had no effect on the constant EF method and the constant  method and led to a very small variation (<1%) of the daily LE estimates in the other three methods. A perturbation of 1 °C in instantaneous and daily air temperatures had a very limited effect (0.3% variation of daily LE estimates) on the constant  method and produced a similar magnitude of variation (-4.2% to 3.7%) of the daily LE estimates in the constant method, the constant Rc method, or the constant Rc/Ra method. A perturbation of 10% in all other inputs resulted in a variation < 1.5% of the daily LE estimates.

Table 1 Sensitivity of the five conversion methods (first column) in estimating daily LE to their inputs (first row). LE i is the instantaneous LE, (R n -G) i is the instantaneous surface available energy, T a,i is the instantaneous air temperature, u i is the instantaneous wind speed, VPD i is the instantaneous vapor pressure deficit, P i is the instantaneous air pressure, hveg is the vegetation height. MD_R is the relative difference, defined as MD (the mean difference of updated daily LE and reference daily LE) divided by the mean of reference daily LE. SD_R is the relative standard deviation, defined as SD (the standard deviation of the difference of updated daily LE and reference daily LE) divided by the mean of reference daily LE. Note that because daily meteorological variables are obtained using the average of multiple half-hourly measurements, the perturbations on instantaneous meteorological variables are also made simultaneously on daily variables. Overall, the constant  method, the constant Rc method, and the constant Rc/Ra method could produce daily LE estimates that are in reasonably good agreement with the ground-based EC measurements whereas the constant EF method and the constant  method have been shown to underestimate the daily LE with large biases and RMSE. The former three methods can all reduce the underestimation of the daily LE that is found in the latter two methods. The lower bias and RMSE in the validation of the daily LEs estimated using either ground-based half-hourly LE without any bias or MODIS-based instantaneous LE with certain degrees of biases demonstrate the robustness of the former three methods and their superiority over the latter two methods. The former three methods are of more solid physical foundation and can capture the effect of temporally variable meteorological factors on the diurnal pattern of surface ET. These three methods (especially the former two) provide good alternatives to the constant EF method and other commonly applied methods for the conversion of remote sensing instantaneous ET to daily values. In view of the strengths and weaknesses of the five developed ET conversion methods, although the evaluation in this study is only focused on a single cropland ecosystem, the findings are instructive. To make general conclusions, more validation work will be conducted under other climate/land cover conditions in the future.

LE i (W/m 2 ) (R n -G) i (W/

  two-source model at 33 clear-sky TERRA overpass times from late April to late September in 2009 in the work of Tang et al. [2011a], (B) the N95 two-source model at 55 clear-sky TERRA overpass times and (C) the N95 two-source model at 46 clear-sky AQUA overpass times from late April 2009 to late October 2011 in the work of Tang et al. [2013a]. These three datasets have been proven to reasonably agree with the ground-based measurements. A positive bias of 1 W/m 2 and a root mean square error (RMSE) of 42 W/m 2 are found in the work of Tang et al. [2011a] when the N95-derived LEs are validation against ground-based large-aperture scintillometer-derived LEs; In the validation of the N95-derived LEs at TERRA and AQUA overpass times in the work of Tang et al. [2013a], biases of 16 W/m 2 and -1 W/m 2 and RMSEs of 46 W/m 2 and 34 W/m 2 are obtained, respectively. These statistics are within the generally acceptable ranges of bias and RMSE. For details about how the three groups of MODIS-based instantaneous LE and R n -G datasets are estimated, please refer to the work of Tang et al.

  Figures 3-6

Figure 1

 1 Figures 7-9

258Figure 2 .Figure 3 .

 23 Figure 3. Comparison of (a) evaporative fraction, (b) Priestley-Taylor parameter, (c) decoupling factor, (d) surface resistance, (e) ratio of surface resistance to aerodynamic resistance at 10:30 h (N=357) and 13:30 h (N=360) local time and those at daily scale estimated with ground-based measurements at the Yucheng station.

Figure 4 Figure 5

 45 Figure 4 Comparison of daily LE estimated using the five conversion methods with ground-based EC measurements corrected using the Bowen ratio (BR) method. (a) Converting 357 half-hourly measurements at 10:30 h local time to the daily scale. (b) Converting 360 half-hourly measurements at 13:30 h local time to the daily scale.

Figure 6 Figure 7 Figure 8

 678 Figure6Comparison of daily LE estimated from 33 N95-derived instantaneous LE at MODIS/TERRA overpass times fromTang et al. [2011a] using the five conversion methods with ground-based EC measurements corrected using the Bowen ratio (BR) method.

  . Applying Eq. (2) to estimate both instantaneous LE (LE i ) and daily LE (LE d ) given meteorological inputs at corresponding time scales, and assuming LE d estimated using appropriately averaged meteorological quantities equals that derived by averaging multiple LE i estimates, one can theoretically link the daily LE to the instantaneous EF, daily surface available energy (R n -G), and other environmental factors with the following equation:

	()	()
			*
	()	()	*

1 Test site

	Yucheng station, located in the southwest of Yucheng County, Shandong province in North China and
	with a latitude of 36.8291° N and a longitude of 116.5703° E, has been measuring continuously the
	long-term exchange of carbon dioxide, water vapor and heat between the land and atmosphere
	(http://www.chinaflux.org/). It is characterized by a subhumid and monsoon climate with mean annual
	temperature and precipitation of 13.1 °C and 528 mm, respectively. Winter wheat is rotated with summer
	corn at this station and the soil type belongs to the sandy loam. Crop height is measured approximately
	every 15 days during the winter wheat and summer corn growth period. Sensors have also been equipped
	to regularly measure surface meteorological and energy flux variables at an half-hourly time interval,
	including air temperature, air relative humidity, wind speed, air pressure, surface 4-component radiation
	(downward and upward shortwave and longwave radiation), and soil heat flux. See the work of Tang et al.

  ) the completely ground-based measurements of surface meteorology, EC-observed half-hourly LE, and R n -G observations without any bias, which can separate the errors induced by the methods from those by the inputs, and (2) the ground-based measurements of surface meteorology and MODIS-based instantaneous LE and R

n -G datasets with a certain degree of bias, which can quantify the accuracy of the derived daily LE by introducing the error caused by the instantaneous LE and R n -G estimates. Moreover, to see if there is any dependence of each of the five methods on the time of ET conversion, the evaluation with the first group of inputs will be conducted at both 10:30 h and 13:30 h local time which approximately correspond to the MODIS/TERRA

  This paper designs the theoretical relationship between daily and instantaneous ETs with a multiplication of multiple fractions through a mathematical derivation of the physics-based Penman-Monteith equation. With rough to rigid assumptions on the designed relationship, this paper further develops five methods for converting remotely sensed instantaneous ET to daily values, one of which is equivalent to the conventional constant EF method that has already been widely applied. The five methods are then evaluated and intercompared using long-term ground-based EC-measured half-hourly LE and three groups of MODIS-based instantaneous LE datasets collected from April 2009 to late October 2011 at the Yucheng station.

	5. Conclusions
						m 2 )	T a,i (°C)	P i (hPa)	VPD i (hpa)	u i (m/s)	hveg (m)
			10%	-10%	5%	-5%	1	-1	10%	-10%	10%	-10%	10%	-10%	10%	-10%
	EF	MD_R (%) SD_R (%)	10.0 8.8	-10.0 8.8	0.0 0.0	0.0 0.0
		MD_R (%) SD_R (%)	10.0 8.8	-10.0 8.8	0.0 0.0	0.0 0.0	0.3 0.3	-0.3 0.3	-0.5 0.5	0.5 0.5
		MD_R (%) SD_R (%)	10.0 8.6	-10.0 8.6	-0.4 0.8	0.4 0.8	3.1 3.0	-3.5 3.5	0.3 1.4	-0.3 1.5	0.8 1.6	-0.9 1.7	0.8 1.6	-0.9 1.7	0.4 1.0	-0.5 1.0
	Rc	MD_R (%) SD_R (%)	8.2 8.8	-8.4 7.8	0.1 1.7	-0.1 2.1	3.8 3.3	-4.2 3.7	0.6 1.6	-0.7 1.6	1.4 1.5	-1.5 1.6	1.4 1.5	-1.5 1.6	0.9 1.1	-0.9 1.1
	Rc/Ra	MD_R (%) SD_R (%)	11.2 10.3	-11.0 9.9	-0.8 1.1	0.8 1.2	2.7 2.7	-3.0 3.2	0.4 1.4	-0.5 1.6	0.4 1.4	-0.5 1.6	0.4 1.4	-0.5 1.6	0.2 1.0	-0.2 1.0

Acknowledgments

The staff members at the Yucheng site are acknowledged for their hard work with the setup and maintenance of the ground-based instruments and data collection. Associate Professor Yuanyuan Jia and Professor Chuanrong Li in the Academy of Opto-Electronics, Chinese Academy of Sciences, are thanked for their cooperation in providing the surface measurements. Meteorological and energy flux data can be acquired at Yucheng National Agriculture Ecosystem Observation and Research Station (http://yca.cern.ac.cn/) after registration and application. This work was partly supported by the National Natural Science Foundation of China under Grant 41571351 and 41571367 and by the International Science & Technology Cooperation Program of China under Grant 2014DFE10220.

particular, since the constant  method, the constant Rc method, and the constant Rc/Ra method require air temperature, wind speed, air vapor pressure, air pressure at both instantaneous and daily (estimated as the average of multiple half-hourly measurements) scales as inputs, these three methods can capture the effect of temporally variable meteorological factors on the diurnal pattern of surface ET. With a more rigid assumption, these three methods can evidently improve the daily ET estimates, which are expected, compared to the constant EF method and the constant  method that may be oversimplified.

Three of the five proposed methods, namely the constant EF method, the constant  method, and the constant Rc method, have already been separately attempted by some authors for converting instantaneous ET to daily values. The designed relationship between daily and instantaneous ETs as shown in Eq. ( 7) in this study physically connects these ET conversion methods with each other. The underestimation of the daily ET in the constant EF method as shown in this study has also been widely reported by a number of authors [START_REF] Delogu | Reconstruction of temporal variations of evapotranspiration using instantaneous estimates at the time of satellite overpass[END_REF]Van Niel et al., 2011;[START_REF] Cammalleri | Applications of a remote sensing-based two-source energy balance algorithm for mapping surface fluxes without in situ air temperature observations[END_REF][START_REF] Chávez | Daily evapotranspiration estimates from extrapolating instantaneous airborne remote sensing ET values[END_REF]. Some authors [START_REF] Brutsaert | Application of self-preservation in the diurnal evolution of the surface energy budget to determine daily evaporation[END_REF]Van Niel et al., 2011] have suggested multiplying additional calibration factors in the formulation of the constant EF method to correct the underestimation of the daily ET.

However, these corrections are generally more empirical and less physically based, which is different from the correction from this study that is of more physical foundation (e.g., the constant method). The constant  method is rarely investigated for the instantaneous ET conversion. One example is from Crago [1996] who once made an attempt to estimate daytime ET from the Priestley-Taylor equation using midday  instead of daytime average values. The author also found an underestimation when compared to the daytime ET measurements and the results produced using the constant EF method, which is consistent with the results obtained from the constant  method in this study. The seldom applied constant Rc method is also reported by [START_REF] Liu | Comparison of evapotranspiration temporal scaling methods based on lysimeter measurements[END_REF] to outperform the constant EF method. The better performance of the constant Rc method is partly attributed to the fact that the sensitivity of this method to surface resistance is lower than that of the constant EF method to evaporative fraction, which can be seen from Section 4.1 and 4.2. Note that Tang et al. [2013a] found that the constant reference EF method had a better performance than the constant EF method. Whether the other four alternative methods are better than the constant reference EF method is beyond the scope of our paper. We will make comparisons between our new methods and the constant reference EF method in future work.

Each of the five methods developed in this study has its own strengths and weaknesses. The constant EF