Mael Arnaud

Carole Adam
email: carole.adam@imag.fr

Julie Dugdale

The role of cognitive biases in reactions to bushfires

Keywords: Multi-agent modelling, social simulation, cognitive biases, BDI paradigm, Victoria bushfires

Human behaviour is influenced by many psychological factors such as emotions, whose role is already widely recognised. Another important factor, and all the more so during disasters where time pressure and stress constrain reasoning, are cognitive biases. In this paper, we present a short overview of the literature on cognitive biases and show how some of these biases are relevant in a particular disaster, the 2009 bushfires in the South-East of Australia. We provide a preliminary formalisation of these cognitive biases in BDI (beliefs, desires, intentions) agents, with the goal of integrating such agents into agent-based models to get more realistic behaviour. We argue that taking such "irrational" behaviours into account in simulation is crucial in order to produce valid results that can be used by emergency managers to better understand the behaviour of the population in future bushfires.

Introduction

The bushfires in Victoria, Australia, on February 7, 2009 (also known as Black Saturday) caused 173 deaths and 414 injuries. Most of the victims were badly prepared to face a fire of such severity and were caught out by surprise [START_REF] Teague | Victorian 2009 bushfire research response final report[END_REF][START_REF] Thornton | Short communication on research response to the black saturday (7th february 2009) victorian bushfires, australia[END_REF]. The population's behaviour before and on that day is still not fully understood and is sometimes referred to as being irrational (i.e. people did not behave according to what would objectively be in their best interests). This was surprising since most of the victims had lived in high fire-risk areas for many years and were aware of the safety issues. The emergency services expected most of the population in the affected area to evacuate before the fire arrived. This was not the case, highlighting a problem with Victoria's crisis management plan, including the communication with the public.

Agent-based modelling and simulation (ABMS) is a technique from Artificial Intelligence (AI) that provides us with a tool to model human behaviours and to test the effect of several parameters. By specifying the attributes of each individual (e.g. stress, exhaustion, knowledge, and also fire plans, etc.) at the micro-level, we can observe the overall behaviour during fires at the macro-level (e.g. the number of people who escape the fire, number of deaths). The proposed approach is to apply ABMS to the field of crisis management in order to improve evacuation plans. The application of such a technique has been used previously [START_REF] Pan | A multi-agent based framework for the simulation of human and social behaviors during emergency evacuations[END_REF][START_REF] Cardon | A multi-agent model for cooperative communications in crisis management systems: The act of communication[END_REF][START_REF] Dugdale | Simulation and emergency management[END_REF] and it is still a very active area of research. One of the most recurrent issues is the level of complexity of the agents; should humans be modelled with simple rules, following the KISS (Keep It Simple, Stupid) principle advocated by [START_REF] Axelrod | The complexity of cooperation: agent-based models of conflict and cooperation[END_REF], or is it better to create more complex agents that are closer to reality, following the KIDS (Keep It Descriptive, Stupid) principle advocated by [START_REF] Edmonds | From kiss to kids -an 'anti-simplistic' modelling approach[END_REF]?

The specific difficulty of choosing an agent's level of complexity when trying to model complex human-like agents has already been discussed [START_REF] Adam | Bdi agents in social simulations: a survey[END_REF][START_REF] Dugdale | Human behaviour modelling in complex socio-technical systems[END_REF]. These authors advocate that an agent trying to mimic human behaviour can not be efficiently modelled with simplistic rules. They concluded that the Belief-Desire-Intention (BDI) agent architecture offers some appreciable features such as: "adaptability, robustness, abstract programming and the ability [for agents] to explain their behaviour."

These features are an undeniable asset in order to model and understand the behaviour of the Victorian population during a fire event. Nonetheless, as stated by [START_REF] Norling | Folk psychology for human modelling: Extending the bdi paradigm[END_REF], the BDI architecture does not capture many aspects of human behaviour and reasoning. It therefore needs some additional work in order to better mimic human behaviour and serve as a grounding model for social agents [START_REF] Frank | From Autistic to Social Agents[END_REF]. Throughout this paper we argue that part of this additional work should 1 deal with cognitive biases. We advocate that they play an important role in human behaviour and need to be taken into account when developping a model, especially during crisis situations.

Cognitive biases are known to be mechanisms widely used by the human brain and which are sometimes unadapted to the situation, leading to mistakes or inaccuracies. Cognitive biases are believed to be found in any strategic decision process [START_REF] Das | Cognitive biases and strategic decision processes: An integrative perspective[END_REF]. They are also found in decision-making processes in uncertain situations [START_REF] Tversky | Judgment under uncertainty: Heuristics and biases[END_REF]. Strategic decision making and deciding under uncertainty are typical cognitive reasoning mechanisms undertaken by people in crisis situations such as bushfires [START_REF] Adam | Modelling the tactical behaviour of the australian population in a bushfire[END_REF]. In addition, crisis situations impose a time constraint on reasoning. Therefore strategic decision making and reasoning with imperfect information in limited time are common, making cognitive biases more likely to happen.

Our overall goal is to build a BDI model [START_REF] Adam | Bdi modelling and simulation of human behaviours in bushfires[END_REF] of human behaviour in crisis in order to improve social simulations by better mimicking human behaviour. In light of the information above, we can see that cognitive biases strongly affect human behaviour during crisis situations. Specifically, they can be the cause of biased perceptions and/or judgements, leading to dangerous behaviours for oneself and reliant others. As a result, we claim that their integration in agent models will improve social simulations of crisis situations. The first goal of this paper is to prove this impact of cognitive biases in crisis situations by identifying some well-known cognitive biases in the victims' testimonies of the Black Saturday event. The second goal is then to formalise these cognitive biases in terms of BDI algorithms, in order to make a first step towards their integration in an agent model for social simulation.

Similar work of integrating cognitive biases in a model has already been performed in the domains of health [START_REF] Voinson | Beyond rational decision-making: Modelling the influence of cognitive biases on the dynamics of vaccination coverage[END_REF] and national defense [START_REF] Kulik | Modeling adversaries and related cognitive biases[END_REF]. However none of these models use the BDI paradigm, which is central in our approach.

The following section presents our data set and the methodology used for data extraction. A presentation of the BDI paradigm follows, with an explanation about the required architecture to implement our BDI model of cognitive biases. We then describe our formalisation of three cognitive biases in the form of algorithms, and illustrate these biases with examples from our data set. Finally the conclusion discusses limits of this work and compares our approach to the literature.

Finding and extracting data

The first task in order to ascertain whether or not cognitive biases played a part in Black Saturday victims' behaviour is to find relevant data. Black Saturday was the worst fire event Victoria ever suffered, consequently casualties and material losses were severe. As a result the state of Victoria created several work groups to understand what happened. Two of them are the 2009 Victorian Bushfires Royal Commission (VBRC) and the Bushfire Cooperative Research Centre (Bushfire CRC). These groups drew data from what they could find (e.g. flora, fauna, victims interviews stating their feelings and memories, police hearings, and general state of the land) and wrote detailed reports [START_REF] Teague | Victorian 2009 bushfire research response final report[END_REF][START_REF] Teague | Final report[END_REF]. The data contained in these reports were extensively used in the scope of this work.

Post Black Saturday reports

Particular attention has been given to the fourth volume of the VBRC final report [START_REF] Teague | [END_REF]. It contains 100 statements from lay witnesses of the Black Saturday events, ordered alphabetically by the witness' name. Statements are heterogeneous in terms of content and source (e.g. testimonies from firefighters who helped during the events, information about the physical and mental state of victims from nurses who came later to help, testimonies of individuals focusing on their struggle with the insurance companies, testimonies of Black Saturday events from family members who suffered a human loss, and detailed testimonies of the day from people who survived the events.) They are narrative transcriptions of oral statements with attached evidence (e.g. photos, maps). Statements are divided into numbered paragraphs and attempts have been made by the interviewer to create consistent sections throughout the statements when possible (e.g. fire plan, the property, views previous to Black Saturday, views during Black Saturday).

The bushfire CRC Final report [START_REF] Teague | Victorian 2009 bushfire research response final report[END_REF] has also been studied in depth. Sections about human behaviour helped in the formulation of the hypothesis relative to the importance of cognitive biases (e.g. by highlighting the importance of environmental cues in alerting Victorians and thus the unconscious concealment of other cue types). This report was also used for the statistics that it contains about the Victorians intentions and actions during Black Saturday. These statistics were compared to those found in a 2010 survey about the behaviour that Victorians would adopt on Code Red (i.e. worst conditions for bushfires) days [START_REF] Research | Behaviour and intentions of households on code red days[END_REF], in order to form a more accurate idea of how Black Saturday affected the Victorians representations of a fire event. This second report concludes by stating that only 3% of Victorians would leave on a Code Red day, even though they aware that authorities' advice is to leave early on those days. Only 15% would stay and defend. This leaves 82% of Victorians in a "wait and see" state, which is the reason why so many Victorians were trapped during Black Saturday fires.

More on cognitive biases

Cognitive bias is a broad and poorly defined concept that encompasses roughly a hundred effective cognitive biases (see [START_REF] Benson | Cognitive bias cheat sheet[END_REF] for a large but non-exhaustive list). Some are well known, while others are merely suspected. Some are known to be groups of cognitive biases (e.g. the Risky Shift Phenomenon is a cognitive bias discovered in 1960, stating that decisions made as a group are less conservative than decisions made by the average group member [START_REF] Shaw | Group Dynamics: The Psychology of Small Group Behavior[END_REF]; this can in fact be caused by other, more specific, cognitive biases). Some are more concerned with affection (loving) [START_REF] Reyna | Numeracy, ratio bias, and denominator neglect in judgments of risk and probability[END_REF][START_REF] Kahneman | Representativeness revisited: Attribute substitution in intuitive judgment. Heuristics and biases: the psychology of intuitive judgement[END_REF])than cognition (thinking). Nonetheless all cognitive biases have two things in common.

First they all serve a common purpose. They help the brain to do its work faster and/or longer, often by using low-cost mechanisms to make decisions or to filter the amount of information gathered by the brain at any time. For example, the "Attribute substitution" mechanism enables us to give the answer to an easy question when confronted with a difficult one [START_REF] Kahneman | Representativeness revisited: Attribute substitution in intuitive judgment. Heuristics and biases: the psychology of intuitive judgement[END_REF] (e.g. when asked the question "How far is the mountain ?", if one does not know the answer, one will answer the question "How blurred is the mountain compared to the ambient haziness?" instead.)

Second they can be the source of mistakes. Since their purpose is to help the brain to make a decision faster or to ignore information, it is not surprising to find that these biases can sometimes lead to inaccurate decisions. Nonetheless it is worth noting that despite the denomination of "cognitive biases" inaccuracies seem to occur only in specific, rather uncommon, situations [START_REF] Pohl | Cognitive illusions : a handbook on fallacies and biases thinking, judgement and memory[END_REF].

Examining the testimonies

Cognitive biases are a wide and heterogeneous family; hence the goal was to find out more about which specific cognitive bias could be found in Black Saturday testimonies. For this purpose we went manually through 30 of the testimonies gathered by the VBRC. Since little attention has been given in the past to identifying cognitive biases in testimonies of populations during crisis situations, no tool exists yet to automatically analyse such interviews. Therefore a new method had to be designed.

Half of testimonies were ignored, since they could not be of any help (i.e. the interviewee was not talking specifically about the Black Saturday events). The other half were searched for situations where survivors or deceased people put themselves at risk. Each such dangerous situation was isolated and we looked for the decision which could have led to it. Then this decision was interpreted according to a set of well-established cognitive biases. For example Edward Cherry is in a dangerous situation (p.16) when outside of his house during an ember attack (ember attacks precede the fire front, which is the most dangerous part of a bushfire event). He took the decision to water the roof of his house a bit longer , while his wife was "shrieking at him to come inside", before suddenly becoming aware that everything around him was on fire. This is likely to be caused by an Optimism bias (i.e. a cognitive bias which lead people to under-estimate the risk of a given situation they are involved in compared to the estimation they would make if not involved). It is worth noting that at least one cognitive bias or set of cognitive biases potentially leading to each dangerous situation were found. Sometimes several unique sets were found.

In the following example, several cognitive biases could led to the decision. Brett Savage in Michelle Buntine's testimony [START_REF] Teague | [END_REF] evacuates his property after having tried to defend it (p. [START_REF] Teague | Final report[END_REF][START_REF] Teague | [END_REF]. Earlier, he did not listen to his partner in life, Michelle Buntine, when she told him repeatedly to evacuate (p. [START_REF] Savion | Clinging to discredited beliefs: the larger cognitive story[END_REF][START_REF] Slovic | The Affect Heuristic[END_REF]. He also received a call from a friend who is a firefighter and who, in order to make him leave, explained to Brett what would happen during the next hours if he stayed (p. [START_REF] Sunstein | Dreadful possibilities, neglected probabilities[END_REF][START_REF] Taillandier | A situated bdi agent architecture for the gama modelling and simulation platform[END_REF]. He stayed and fought the fire for some time before having to evacuate during the fire event.

In terms of cognitive biases it is hard to detect what played a part in Brett's decision to stay and fight. It could be the Conservatism bias (i.e. a slow update of his beliefs that he would be safe while defending his property), the Semmelweis Reflex (i.e he clung to his belief, even with compelling evidence that it was false), an Anchoring effect (i.e. he was committed to the idea to defend his house), the Optimism bias (i.e. he though he was not at risk in this situation while someone else would have been) or the Overconfidence effect (i.e. he considered his beliefs as more accurate than the ones from his partner and friend). The most simple, robust, and consistent with the psychology literature sets were kept. However, we acknowledge that some may have been missed.

Retained cognitive biases

The use of our method revealed that some types of cognitive biases were found more often than others: biases about 1) beliefs (i.e. biases acting in favour of, or against, the update of a previous belief), 2) affect (i.e. biases favouring the option in which something one likes could be preserved over the option in which one is in a safe place) and 3) bad probability estimation (i.e. some options are seen as far more/less probable than they really are).

Three cognitive biases were chosen, according to this finding and for two other reasons: biases chosen are relevant to each other (i.e. the same tools can be used to model the three of them, and their interaction creates a logical model of information processing); they are easily adaptable to the BDI paradigm, which makes an extensive use of the notion of belief. The three biases are: 1) The Neglect of Probability bias, which belongs to the bad probability estimation category, 2) the Semmelweis Reflex and 3) the Illusory Truth effect. The last two biases belong to the belief updates category. No cognitive bias found in the affection category satisfied the conditions and so have not been included.

3 Proposed BDI model of cognitive biases

The BDI paradigm

The BDI paradigm describes agents in terms of their mental attitudes (Beliefs, Desires, Intentions), which are "folk psychology concepts that straightforwardly match human reasoning as people understand it, making the models easier to design and to understand" [START_REF] Adam | Bdi agents in social simulations: a survey[END_REF].

1. Beliefs represent an agent's knowledge about the world (e.g. road 45 is blocked, ember attacks precede the fire front).

2. Desires are the goals of an agent, i.e. their preferred states (e.g. be close to one's children). They can be inconsistent (e.g. during an ember attack, the agent might both want to defend its house and to flee the fire). Choosing between desires is the role of a reasoning engine [START_REF] Norling | Creating interactive characters with bdi agents[END_REF], that remains to be chosen in this work.

3.

Intentions are what an agent is committed to do. They are basically refined, practical desires. They have to be consistent with each other, and should not be dropped easily. The agent usually has a library of plans (sequences of actions) allowing it to achieve its intentions.

Required agent model

In this section we describe the required minimal architecture for an agent to be able to implement the cognitive biases.

We do not provide a conceptual agent model, but give a minimal set of requirements for an agent architecture to be able to implement the cognitive biases algorithms in this paper.

• A belief operator with associated subjective probability, ranging from 0 (certainly wrong) to 100 (certainly true). The addition of subjective values of a belief and its opposite sum to 100. A belief with a probability of 50 means that the agent is completely unsure.

• A belief base that stores beliefs.

• Psychological attributes, such as level of risk aversion.

• A table of occurrences of received information (counting how many times the same information have been received)

• A function getBeliefProbability (Belief ϕ) that returns the probability of a given belief.

• A function saveBeliefProbability (Belief ϕ, Number α) that updates the probability of a given belief in the agent's belief base.

• A function incrementNumberOfOccurrences(Information ϕ) that increments by 1 the number of times a given information has been gathered by the agent.

• A function getAcquiredInfoOccurrences(Information ϕ) that returns the number of times the agent has gathered a given information.

• A function acquireBelief(Belief ϕ, Number α) that saves a given belief and associated probability to the agent's belief base.

• The functions dramaticallyIncreaseBeliefProbability (Belief ϕ, Number α) and decreaseBeliefProbability (Belief ϕ, Number α) that modifies the probability of a given belief.

This minimal required architecture may be provided by PLEIAD (an affective agent coded in Prolog [START_REF] Adam | A BDI emotional reasoning engine for an artificial companion[END_REF]) or by GAMA (an agent-based simulation platform [START_REF] Grignard | Gama v. 1.6: Advancing the art of complex agent-based modeling and simulation[END_REF] recently enriched with a BDI architecture for the agents [START_REF] Taillandier | A situated bdi agent architecture for the gama modelling and simulation platform[END_REF]).

Model of the three biases

In this section we provide a generic model of three cognitive biases using the architecture described above. Only pseudo-code is described so as not to commit to a particular implementation language.

Neglect of Probability

We formalise the Neglect of Probability bias in algorithm 1. We begin by explaining what we mean when using the expression "are perceived to be...", then we detail this bias and its mechanisms. Uses of the expression "are perceived to be ..." in the formalization of the Neglect of Probability bias are shortcuts for two statements.

• The consequences implied by this belief could be dire or extremely favourable (e.g. for agent A believing that road R is on fire implies that he could not reach his home, this will leave his home unprotected and at risk of probable burning; which is a dire event).

• The risk aversion or risk seeking value of the agent makes him perceive the consequences as extremely favourable/unfavourable, as described in [START_REF] Kahneman | Prospect theory: an analysis of decision under risk[END_REF].

The Neglect of Probability bias is composed of three mechanisms. Two of them target low probability beliefs while the third one targets high and medium probability beliefs.

• The first mechanism (described in [START_REF] Reyna | Numeracy, ratio bias, and denominator neglect in judgments of risk and probability[END_REF]) is a way to ignore what is perceived both as unlikely to happen and as having no consequences. It is formalized on lines 9-10 of algorithm 1. It reads: if the agent estimates something only has a low chance of being true and has no consequences, then the agent considers it as false.

• The second mechanism (described in [START_REF] Sunstein | Dreadful possibilities, neglected probabilities[END_REF]) is a way to anticipate an event that would greatly impact one's life and thus enables one to prepare for it. It is formalized on lines 11-12 of algorithm 1. It reads: if the agent estimates that something has a low chance of being true but either desires or dreads it, then the agent considers that it has a substantial chance of being true.

• The third mechanism (described in [START_REF] Tversky | Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment[END_REF][START_REF] Kahneman | Prospect theory: an analysis of decision under risk[END_REF]) reduces the perception of high and medium probabilities. It is formalized on lines 13-14 of algorithm 1. It reads: if the agent estimates something has a high or medium chance of being true, then the agent under-estimates its probability of being true.

Algorithm 1 Pseudo-code for the Neglect of Probability bias 1: procedure updateBeliefProbability (info, perceivedProbability )

2:
ancientBeliefProbability ← getBeliefProbability (info) if newBeliefProbability is small and consequences are not perceived to be dire and consequences are not perceived to be extremely favourable then else if beliefProbability is small and (consequences are perceived to be dire or consequences are perceived to be extremely favourable) then saveBeliefProbability (info, newBeliefProbability) 17: end procedure

Alice Barber

Alice Barber is a woman who survived the events but was injured. She lost her house. No children or partner in life are recorded. She likes to garden and therefore her house is surrounded by vegetation. Prior to the event she possessed a fire plan, i.e. go to a place that she scouted earlier and identified as a potential shelter, and a fire plan trigger, i.e. act according to the fire plan as soon as the power is cut in the house.

• The dangerous situation is the fact that she lives in a high risk area with a weak fire plan trigger.

• The decision leading up to the situation is to choose a weak fire plan trigger.

• The Neglect of Probability is highlighted when she testifies about her mental attitude: "what will happen, will happen" (p. 7). She does not want to bother herself with costly fire preparations and does not consider a fire event as dire. Plus she has good reasons to believe that her fire plan trigger is good. Thus neglecting the probability of such an event.

This situation could be modelled by one agent as follows:

• Beliefs: Fire plan will be triggered before a fire is detected (100)

• Desires: Be safe, Be close to the house

• Intentions: Stay close to the house until the fire plan triggers, then follow fire plan

• Risk aversion: Low

Andrew Paul Trenwith Berry

Andrew Berry is a married man who survived the events with his wife, Nicole, and his father. Although Andrew and Nicole made relevant decisions regarding this case, they lost their house. Prior to the events Andrew possessed a house with a sprinkler-based defense system (considered as the best anyone can do (p. 14) by some Country Fire Authority (CFA) members) and a bunker that was close to the house that was large enough to accommodate a dozen people. The fire plan was to stay and defend. The family also experienced fire in 2006. This experience raised their risk aversion. This example is reversed, since the Neglect of Probability saved the family.

• The safe situation is the fact that Andrew and Nicole were able to shelter inside the bunker while their house burnt.

• The decision leading up to the situation is to have a the bunker built in the yard, despite a good house defense system.

• The Neglect of Probability underlies the decision of building the bunker. The 2006 fires raised Nicole and Andrew's father risk aversion. Thus the probability associated to the belief of experiencing a fire strong enough to threaten their lives while sheltered in their apparently well-defended house were overestimated (weather conditions during Black Saturday were unique and very unlikely).

This situation can be modelled with a single agent as follows:

• Beliefs: House is safe (60), Bunker is comfortable (0), Bunker is safe (70)

• Desires: Be safe, Be comfortable

• Intentions: Stay safe in the house before and during the fire front, then defend it. If not safe in the house, go to the bunker.

• Risk aversion: High

Fiona Wallace

Fiona has a partner in life named Heather and they both survived Black Saturday. No children are recorded as being involved. They are both Victorians, living in low fire-risk areas. They went to a Bed and Breakfast (B&B) hostel located in a high fire-risk area during Black Saturday. They both were aware of the warning issued by the authorities during the days prior to Black Saturday.

• The dangerous situation occurs when the fire reaches the B&B they are staying in and they have to defend it.

• The decision leading up to the situation is the decision to go on a trip in a high fire risk area while knowing about the hazardous weather conditions.

• The first Neglect of Probability underlying this decision occurs when Fiona and Heather hear the news about the weather: "the comparisons to Ash Wednesday emphasised the severity of the risk and we knew that it was going to be an extremely bad fire danger day." (p. 3). The probability of a fire being high in the information received is being neglected and is considered as medium rather than high.

• The second Neglect of Probability underlying this decision occurs when Fiona and Heather reason about the probability of having their particular B&B being attacked by fire in such a large area: "We reasoned that even when there is a major fire, a huge amount of rural Victoria does not get burnt." (p.4). This probability ends up being low. Since their aversion to risk is also low the probability associated to the belief of being caught in a fire event is neglected.

This situation can be modelled with a single agent, as follows (beliefs in italic can be omitted if a reasoning engine allows agents to build their own beliefs this way):

• Beliefs: B&B is relaxing (80), B&B is prone to fires (45), B&B will experience a fire event during the trip (0)

• Desires: Be safe, Be relaxed

• Intentions: Go to a safe and relaxing place.

• Risk aversion: Low

Semmelweis Reflex / Belief Perseverance

The Semmelweis Reflex, also called Belief Perseverance, is a cognitive bias in which people cling to their beliefs even when they face proofs they are not true [START_REF] Anderson | Abstract and concrete data in the perseverance of social theories: When weak data lead to unshakable beliefs[END_REF]. The Semmelweis Reflex is formalized in algorithm 2, based on an explanation given in [START_REF] Savion | Clinging to discredited beliefs: the larger cognitive story[END_REF]; stating that a certainty is harder to update than a belief one thinks is only probable. One of the ways to "overcome" this bias has been suggested (p. 85 of [START_REF] Savion | Clinging to discredited beliefs: the larger cognitive story[END_REF]). This has been modelled in order for the agents to eventually update their certainty. The way to overcome the bias is based on the repetition of information (e.g. if an agent is certain of ϕ it needs to get the information ¬ϕ a certain number of times before it will be able to update its former certainty). This is consistent with the Illusory Truth formalization.

Algorithm 2 Pseudo-code for the Semmelweis Reflex

1: function testForSemmelweisReflex(info) 2:
if getBeliefProbability (info) = 0 and acquiredInfoOccurrences(info) is not enough then

John Benett

John lives alone, he survived and, with other people, he successfully defended his house. During the whole afternoon, John felt a North wind blowing. At 3pm he received a call from a friend, warning him that a fire was coming from the West to his property. John ignored this warning. Later, he saw people driving dangerously near his property. He did not pick up on these cues either.

• The dangerous situation occurs at 5pm when a fire caught John by surprise. It came from the West while a North wind was blowing.

• The decision leading up to the situation is to ignore cues going against his belief that no fire could come from the West while the wind was blowing from the North.

• The Semmelweis Reflex underlying this decision prevents him from considering cues contrary to his belief that the fire will come from the North, as he states: "I thought that the North wind would prevent the fire from reaching Kinglake West and that it would direct it somewhere else." (p. 7)

This can be modelled in one agent as follows:

• Beliefs: House is safe (100), Fire goes in the same direction as the wind (100), Fire will come from [current wind direction] (100)

• Desires: Be safe, Defend the house

• Intentions: Monitor [current wind direction] side of the land to gather environmental cues about an approaching fire, then proceed to defend the house.

Jim Baruta

Jim is married but his wife was not involved in the events. He survived but lost his house.

• The dangerous situation occurs at 5pm when when he drove on a road during a fire event (p.15).

• The decision leading up to the situation is to to keep driving even though he saw smoke and fire spots on the road.

• The Semmelweis Reflex occurs after at least one other cognitive biases was triggered (e.g. Optimism Bias) to build a certainty about the fact that he would be safe travelling home even though he knows he should not be doing it: "[in case of fire] you can't get on the roads, that is the last thing you should do" (p. 10). The Semmelweis Reflex prevents him considering cues that are contrary to his belief that he will be safe on the road.

This can be modelled in one agent as follows:

• Beliefs: The road home is safe (100), Do not be on the road during a fire event (80)

• Desires: Be safe, Defend the house

• Intentions: Go home then proceed to prepare and defend the house.

• Risk aversion: Extremely low

Illusory Truth

The Illusory Truth bias was shown for the first time in 1977 [START_REF] Hasher | Frequency and the conference of referential validity[END_REF] and has proven to be quite robust. Its effect is straightforward: the more one hears some information, the more one is inclined believe that the information is true. The Illusory Truth effect also ignores prior knowledge [START_REF] Fazio | Knowledge does not protect against illusory truth[END_REF], which makes it easier to formalize. It is formalized in algorithm 3, on lines 8-12. It reads: if the current agent already possesses a belief relative to the last information it gathered, then reinforce the belief according to the credit it puts in this information, multiplied by the number of times it gathered it. This has been implemented regarding processing fluency [START_REF] Fazio | Knowledge does not protect against illusory truth[END_REF]. According to the author the Illusory Truth would come from the fact that repetition makes information easier to understand. Processing fluency states that the easier something is to understand the more truthful it appears. In our algorithm, on line 10, the probability associated with an information perceived is linked to the number of times this same information has already been perceived.

Algorithm 3 Pseudo-code for the Illusory Truth effect 1:

# ϕ is an information given by the environment to an agent 2: info ← perceive(ϕ) 3: perceivedProbability ← perceiveProbability (ϕ) 4: incrementNumberOfOccurrence(info) if not testForSemmelweisReflex(info) then end if 13: end if

Peter Ross Brown

Peter Brown is a married man with three children (aged 20, 18 and 16). He lives with his wife and children in their own house with a pool. The pool is intended to serve as a water tank in case of a fire event. During Black Saturday Peter's oldest child was away. Peter also listened to ABC radio during the entire day. The whole family survived the events but lost the house.

• The dangerous situation occurs when the family members are gathered in and around the pool and the fire unexpectedly strikes.

• The decision leading up to the situation is for the family not to evacuate and not to prepare the house before the fire arrived. Peter was trying to connect the fire pump to the pipes when it did.

• The Illusory Truth makes Peter believe in the accuracy of ABC announcements, since the ABC announcer repeated that they provided the most up-to-date source of information concerning the bushfire (p. 16). Next Peter reasons that since there was no warning from ABC for his area it means that his house and family are not threatened.

This situation can be modelled with a single agent as follows:

• Beliefs: ABC Radio provides up-to-date information (100), No fire is detected in my area (100)

• Desires: Be safe, Defend the house, Do not prepare the house if not needed

• Intentions: Monitor for a threat by listening to the best radio channel found and looking at the environment, proceed to prepare the house if a fire is detected.

• Risk aversion: Medium

Michael Halls

Michael is the father of Natasha Davey. His daughter died during the Black Saturday along with her family. The family was sheltering inside their house, which had been well prepared and was defended by Natasha's husband.

• The dangerous situation occurs when the family is in the house while a fire is coming.

• The decision leading up to the situation is to stay and defend the house.

• The Illusory Truth makes Natasha believe that a well-prepared and defended house is a safe place in case of a fire event. Michael Halls testifies that his daughter's family has been reading brochures, comparing what they were going to do in the face of a fire to what their neighbours were going to do (which was more), and went to CFA meetings (p. 7 -13, 29). Furthermore, the CFA brochures they consulted implied that if one is well prepared, one has nothing to fear from a fire (p. 38, "Why does the bushfire guide show pictures of children protecting a property?").

This situation can be modelled with a single agent as follows:

• Beliefs: The house is well prepared (80), I can defend the house (80), My husband can defend the house (80), A well-prepared and defended house is safe (100), The house is comfortable (80)

• Desires: Be safe, Have the children in a safe area, Have the children being comfortable

• Intentions: Monitor fire threat from inside the house. In case of a fire event, shelter in the house then defend it.

• Risk aversion: Medium-High

Conclusion and future work

Psychology and cognitive science related works show that cognitive biases affect human behaviours in crisis situations, where uncertainty or stress factors are present. Examples of individuals putting themselves, their friends or their family at risk by acting in a way that was not anticipated by decision-makers have been extracted from a concrete set of data. These behaviours were then connected to cognitive biases. Three specific cognitive biases have been formalized into algorithms, which are consistent with their related bias description in the literature. We argue that implementing these algorithms in BDI agents can make them more realistic by addressing some of BDI core issues (as identified by [START_REF] Norling | Folk psychology for human modelling: Extending the bdi paradigm[END_REF]) in terms of 1) decision making, 2) inaccuracies and 3) situation awareness of agents. This work though should be considered preliminary. We provided algorithms to ease implementation of the biases, which constitutes a good basis for a computational model, but we have not implemented and tested them yet. These algorithms, although not yet implemented constitute a good basis for a computational model and ease implementation.

The methodology used to find occurrences of cognitive biases in our data set should also be treated as a work in progress. Since it is not based on any scientifically-grounded model of cognitive biases (we could not find any both exhaustive and reliable), it relies on disparate scientific evidence. Results are therefore based on a subjective interpretation of the testimonies.

Scarce examples of models integrating cognitive biases can be found. This work can be compared to two of them. The first is in the field of national defense [START_REF] Kulik | Modeling adversaries and related cognitive biases[END_REF], while the other is in the field of health [START_REF] Voinson | Beyond rational decision-making: Modelling the influence of cognitive biases on the dynamics of vaccination coverage[END_REF].

The national defense model aims to predict a target's reaction to "Effect-Based Operation" (EBO) (e.g. the 9/11 events in the U.S.). It is based on a "Synthetic Cognitive Modelling" (SCM) approach, which takes several factors into account and gives probabilistic results. While their work aims to predict how an EBO would affect a target, we are trying to understand why a population reacts the way it does in a crisis situation. This explains the use of different paradigms. We make use of a white box (i.e. something we can see into) paradigm (BDI), in order to explain behaviours. Eventually we would like to build a serious game to experiment with the impact of different factors on the population. This work in national defense uses a black box (SCM) paradigm, looking only at inputs (data), and outputs (behaviours). Their approach of cognitive biases also differs from ours, since they do not offer any framework to integrate identified cognitive biases or mind mechanisms in their model.

The model in the health field is based on mathematical functions and thus uses a white box approach. It aims to help understanding why individuals in developed and developing regions can be reluctant to vaccination, even though "vaccination has greatly reduced the burden of infectious diseases worldwide". The authors advocate that models should not assume individuals to be rational, which bring our work close to theirs. This irrationality is modelled using using a standard model made for capturing the disease transmission process, augmented by a belief model and two functions representing two distinct cognitive biases. However, the belief model is far simpler than the one implemented in BDI and only takes into account two parameters for each individual (epidemiological status and opinion). Our work is closer to this model than to the previous one, even though this model is mathematically based. However this work uses the KISS principle, in which things are as simple as possible, while ours is more descriptive.

Two areas for future work are planned. First, more work is needed on the conceptual side of our cognitive biases model in order to refine how it integrates with the underlying formal semantics of BDI agents. Second, we want to implement and test the biases that we have presented in order to validate our hypothesis. The implementation may then be enhanced in several ways. The Belief Perseverance Effect implementation will be complemented by the addition of other ways to overcome the fallacy as described in [START_REF] Savion | Clinging to discredited beliefs: the larger cognitive story[END_REF], along with a way to slow down the belief-updating process (i.e. Conservatism bias). The Illusory Truth Effect will be widened by the implementation of the processing fluency mechanism. In a more general way, this work would benefit from the formalisation of trust, which can affect perceived probabilities. The affective heuristic [START_REF] Slovic | The Affect Heuristic[END_REF] will also be integrated, along with work on an "affective weight" agents give to their environment. This will help us understand how agents integrate and contextualize objects in the world.

4 :

 4 else # getBeliefProbability (info) > 0 or acquiredInfoOccurrences(info) is enough

Acknowledgements

This research was funded by the University Grenoble-Alpes through AGIR project SWIFT (2016-2019), and by Grenoble Pôle Cognition (2017).


N Guillou

G Chapalain
email: georges.chapalain@developpement-durable.gouv.fr

E Duvieilbourg
email: eric.duvieilbourg@univ-brest.fr

Modelling impact of bottom roughness on sea surface temperature in the Sea of Iroise

Keywords: Ushant front, tide, wave, COHERENS, SWAN, SIRANO

Modelling impact of bottom roughness on sea surface temperature in the Sea of Iroise

Nicolas Guillou, Georges Chapalain, Eric

Introduction

The Sea of Iroise is a shallow environment (Fig. 1) located at the western end of french Brittany with strong tidal currents reaching 4 m s -1 near the isle of Sein (e.g., SHOM, 1968;Mariette et al., 1982). This intense hydrodynamic results in water depths between 50 and 90 m in a well-mixed water column with extremely weak temperature variations between the surface and the bottom whenever restratification associated with atmospheric fluxes is not able to overcome the effect of mixing [START_REF] Mariette | Simulation of the formation of Ushant thermal front[END_REF]. In spring and summer, a strong stratification establishes with the generation of offshore and nearshore thermal fronts such as the dominant Ushant front appearing at the west of the isles of Sein and Ushant which separates tidally mixed coastal waters from thermally stratified offshore waters (e.g. [START_REF] Pingree | Survival of dinoflagellate blooms in the western English Channel[END_REF][START_REF] Boyer | Observations of the Ushant tidal front in September 2007[END_REF].

In addition to field observations (Le Corre and Mariette, 1985), numerous models have largely contributed to a better knowledge of the formation of these thermal structures. The roles of barotropic tides and wind-induced vertical mixing have been revealed by unidimensional (1D) [START_REF] Altazin-Pichon | Application d'un modèle de thermocline à la formation du front thermique en mer d'Iroise. Confrontation des résultats avec des mesures in situ[END_REF][START_REF] Mariette | Effet des échanges atmosphériques sur la structure thermique marine. Application à des zones du large et à une zone côtière[END_REF] and bidimensional (2D) (Mariette et al., 1982;[START_REF] Mariette | Simulation of the formation of Ushant thermal front[END_REF] modelling studies. More recently, three-dimensional (3D) models [START_REF] Cambon | Etude numérique de la mer d'Iroise : Dynamique, variabilité du front d'Ouessant et évaluation des échanges cross-frontaux[END_REF][START_REF] Muller | Etude de la circulation résiduelle langrangienne en mer d'Iroise[END_REF] have focused on the residual and lagrangian water mass transports associated with these hydrological structures. Nevertheless, the influence of bottom-friction parameterizations was poorly addressed. Simulations used to assume uniform bottom-roughness parameters neglecting the effects of the heterogeneous distribution of seabed sediments and the waves in the bottom boundary layer. These aspects deserve however some attention in a region with (i) quite heterogeneous bottom sediments including silts, sands, gravels and rock outcrops (e.g., [START_REF] Hinschberger | Carte sédimentologique sousmarine des côtes de France[END_REF][START_REF] Augris | Atlas thématique de l'environnement marin de la baie de Douarnenez (Finistère)[END_REF] and (ii) significant exposure to North Atlantic wind-generated surface-gravity waves [START_REF] Benoit | A nearshore wave atlas along the coasts of France based on the numerical modeling of wave climate over 25 years[END_REF].

The purpose of the present study is to investigate the effects of bottom roughness parameterization on modelling of sea surface temperature (SST) in the Sea of Iroise. The approach relies on a comparison between numerical predictions and observations. In-situ measurements are realized (i) nearshore along the route of a vessel travelling between the coast and the isle of Ushant and (ii) offshore at two fixed-point stations (section 2.1.1). These observations are completed by SST satellite images (section 2.1.2). Modelling is based on the coupling between a wind-generated surface-gravity wave module (section 2.2.1) and a 3D circulation module integrating the advective and diffusive transports of temperature and salinity (section 2.2.2). Numerical predictions are compared with observations over the period from April to October 2011 when nearshore SST measurements are available (sections 3.1.1 and 3.1.2). These comparisons exhibit (i) the seasonal and spring-neap tidal variabilities of SST and (ii) the main associated-hydrological features such as the dominant Ushant thermal front. Modelling is exploited to conduct a sensitivity study on the effects of the heterogeneous bottom roughnesses associated with (i) the granulometric distribution of seabed sediments and (ii) the apparent friction induced by the wave in the bottom boundary layer (section 3.2). Improvements of numerical predictions with respect to available satellite observations are displayed (section 3.2.1). Spatial and temporal changes in predicted SST are quantified further with mappings of induced differences in the nearshore areas of the Sea of Iroise (section 3.2.2).

Materials and methods

Observations description

In-situ data

Measurements here used were provided by the "Ships-of-Opportunity" (SoO) project SIRANO ("Surveillance des eaux de surface en mer d'Iroise et RAde de Brest par des Navires d'Opportunités"). The principal advantage of SoO systems is to increase the temporal and spatial coverages of in-situ measurements at a fine resolution in the coastal areas (e.g., [START_REF] Petersen | FerryBox and MERIS -Assessment of coastal and shelf sea ecosystems by combining in-situ and remotely sensed data[END_REF][START_REF] Grayek | Use of FerryBox surface temperature and salinity measurements to improve model based state estimates for the German Bight[END_REF]. SoO systems can thus provide valuable information on water and temperature transports over large regions when combined with other observations like remote sensing data. Indeed, nearshore satellite images constitute most of the time a database of scattered observations with a time step often too large to catch surface heating processes like the cooling of surface water (e.g. [START_REF] Grayek | Use of FerryBox surface temperature and salinity measurements to improve model based state estimates for the German Bight[END_REF]. SIRANO operates two times per day SST measurements along the route of the "Enez Eussa III" vessel between Brest and the isle of Ushant (Fig. 1). The instrumentation system consists of a multiparameter probe YSI 6920V2-2-M in direct contact from a continuous flow of seawater taken at a water depth of 1.4 m under the sea surface. The basic sensors measure temperature, salinity, turbidity, pH and chlorophyll-a fluorescence. The observations used in the present study are restricted to the SST. The rate of acquisition is set to 0.1 Hz which provides measurement at an averaged spatial resolution of 100 m. SIRANO integrates also a Global Positioning System (GPS) for the location of the measuring points. This device is connected to a station on shore for data transfer, archiving and dissemination on a web site (http://www.memphys-lgce.fr.ht/). More details about the instrumentation system are given by [START_REF] Duvieilbourg | Observation multiparamètres par navire d'opportunités le long du continuum terre-mer de la rade de Brest et de la mer d'Iroise[END_REF]. Measurements here used were only available till October 2011 as the "Enez Eussa III" vessel was replaced in autumn 2011. Data were processed to extract time series of SST measurements at six fixed-points evenly spaced along the route of the averaged vessel path over the period of interest from April to October 2011 (Fig. 1 and Table 1). The method here retained has consisted in gathering data collected at a distance less than 500 m of these points. Statistical analysis performed on GPS data exhibits the regularity of the vessel path between the harbours of Brest and Le Conquet. Whereas the route is liable to change a little more in its offshore part, the treatment allows to acquire at least one measurement per day at every location.

Point

Coordinates SIRANO observations are complemented by measurements at two offshore wave-buoy stations WB1 (λ = 4.97 o W, φ = 48.29 o N) and WB2 (λ = 5.75 o W, φ = 48.50 o N) (Fig. 1). Both stations are part of a measurement system of waves parameters (significant wave height, period and direction) and SST in the Sea of Iroise. The water temperature sensor is located at each stations in a pocket in the interior of the mooring eye in direct contact with the metal. Measurements were performed at depths of 0.4 and 1 m below free surface at stations WB1 and WB2, respectively. SST data were however missing at both measurement points at the end of the period of interest in relation to malfunction of the instrumentation systems. Wave observations were also lacking: at the end of September 2011 at station WB1 and the end of November 2010 at station WB2.

h

Remote sensing data

Daily-SST remote-sensing data are derived from the observations of the european ocean-SST multi-sensor L3 provided by MyOcean (European Commission) project (http: //www.myocean.eu/). Multi-sensor data are built from bias-corrected L3 mono-sensor products at the spatial resolution of 0.02 o . If the native collated resolution is below 0.02 o , the distributed resolution is reached by averaging the best quality data. If the resolution is over 0.02 o , the collated data are obtained at the nearest neighbour without interpolation nor artificial increase of the resolution. Satellite images are analysed on the basis of the index coverage of available data in the nearshore areas of the Sea of Iroise. A selection of three images is retained for the period of interest illustrating the evolution of SST patterns: in spring (on 25 May 2011), in summer (on 30 August 2011) and in autumn (on 28 September 2011).

Model description

The numerical model couples the Simulating WAves Nearshore (SWAN) module [START_REF] Booij | A third generation wave model for coastal regions, part i, model description and validation[END_REF] with the 3D COupled Hydrodynamical-Ecological module for RE-gioNal and Shelf seas (COHERENS) [START_REF] Luyten | COHERENS: A COupled Hydrodynamics-Ecological model for REgioNal and Shelf seas -Model Description (Available on CD-ROM[END_REF]. COHERENS solves temperature and salinity transport equations. The principal model assumptions are placed on the 3D circulation module. The flow is assumed to be turbulent over a featureless rough bottom characterized by the roughness parameter z 0 defined as the height above the seabed at which the fluid velocity is zero.

SWAN

SWAN solves the time-dependent spectral action balance equation [START_REF] Booij | A third generation wave model for coastal regions, part i, model description and validation[END_REF]. Its accounts for depth shoaling, refraction, non-linear transfer of energy through wavewave interactions and wave-energy dissipation due to whitecapping, bottom friction and depth-induced breaking. The parameterizations adopted for sources and sinks are briefly detailed hereafter. Wave growth by wind is computed with the exponential term of [START_REF] Komen | On the existence of a fully developed wind-sea spectrum[END_REF]. Processes of whitecapping are described with the pulse-based equation of [START_REF] Hasselmann | On the spectral dissipation of ocean waves due to whitecapping[END_REF]. Energy dissipation in random waves due to depthinduced breaking is quantified according to [START_REF] Battjes | Energy loss and set-up due to breaking of random waves[END_REF]. Finally, the empirical model of [START_REF] Hasselmann | Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP)[END_REF] parametrizes the sink term of bottom friction. The wave action balance equation is expressed in a spherical coordinate system. Further details about the mathematical expressions of sources and sinks are available in SWAN technical documentation (SWAN team, 2009).

COHERENS

COHERENS solves (i) the continuity equation and the Reynolds-averaged momentum equations derived using the [START_REF] Boussinesq | Essai sur la théorie des eaux courantes[END_REF][START_REF] Boussinesq | Théorie analytique de la chaleur, mise en harmonie avec la thermodynamique et avec la théorie mécanique de la lumière[END_REF] approximations and the vertical hydrostatic equilibrium and (ii) the 3D transport equations of temperature and salinity. The water density is computed with the general equation of state defined by the Joint Panel on Oceanographic Tables andStandards (UNESCO , 1981). The horizontal eddy viscosity ν H and diffusivity λ H are parametrized following [START_REF] Smagorinsky | General circulation experiments with the primitive equations, i, the basic experiments[END_REF]. The vertical eddy coefficients are expressed as

ν T = S u k 2 / + ν b and λ T = S b k 2 / + λ b
where k is the turbulent kinetic energy, is its dissipation rate and S u and S b are the stability functions. These turbulent moments are obtained following [START_REF] Luyten | Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the Rhine outflow region[END_REF] and [START_REF] Luyten | An analytical and numerical study of surface and bottom boundary layers with variable forcing and application to the North Sea[END_REF] by solving a one-equation k -closure scheme. A transport equation is solved for the turbulent kinetic energy k while the dissipation rate is parametrized according to = 0 k 3/2 /l where 0 = 0.108 3/4 and l is the mixing length computed from the formulation proposed by [START_REF] Blackadar | The vertical distribution of wind and turbulent exchange in a neutral atmosphere[END_REF]. S u and S b are expressed as a function of the stability parameter α N = k 2 /ε 2 N 2 where N 2 is the squared buoyancy. Finally, the background coefficients are taken equal to ν b = λ b = 10 -6 m 2 s -1 .

Coupling with the wave propagation module consists in integrating waves-induced roughness in surface and bottom boundary conditions of momentum and turbulent equations. Boundary conditions are derived from the law of the wall relying on appropriate formulations of sea-surface and apparent bottom-roughness parameters denoted z 0s,ω and z 0b,ω , respectively. Waves effects on sea-surface roughness are computed following the parameterization scheme proposed by [START_REF] Pan | A new parameterization scheme for sea surface aerodynamic roughness[END_REF] ln

z 0s,ω H s = 2.82 ln u * s c p -0.295 (1)
where H s is the significant wave height and c p is the phase velocity of waves at peak period. The surface friction velocity u * s is obtained by specifying the surface stress as a function of the wind velocity |u 10 | at a reference height of 10 m above the sea surface

τ s = ρ a u 2 * s = ρ a C s D |u 10 | 2 (2)
where ρ a is the air density taken equal to ρ a = 1.2 kg m -3 and C s D is the surface drag coefficient given by the law-of-the-wall relationship

C s D = 0.4 ln (10/z 0s,ω ) 2 .
(3)

Waves effects on bottom roughness are computed on the basis of Signell et al.'s (1990) formulation adapted from the original theory of [START_REF] Grant | Combined wave and current interaction with a rough bottom[END_REF] on the interactions between wave and current bottom boundary layers. This formulation has been modified in COHERENS according to [START_REF] Liang | Bottom shear stress under wave-current interaction[END_REF] by introducing the effects of the random wave field and the angle φ cω between the current and wave propagation directions. The apparent bottom roughness parameter felt by the current above the wave boundary layer is thus expressed as

z 0b,ω = δ |1-u * c u * cω | ω z | u * c u * cω | 0 (4)
where δ ω = 2κu * cω /ω is the thickness of the wave boundary layer, κ is the von Karman's constant taken equal to κ = 0.4 and ω is the wave frequency at the bottom wave period. The friction velocity u * cω arising from the combined wave and current shear stresses is given by

u * cω = u * ω 1 + 2 u * c u * ω 2 | cos φ cω | + u * c u * ω 4 1/4 . ( 5
)
u * ω is the shear velocity associated with the wave and given by u * ω = 1 2 f ω U ω where f ω is the wave friction factor evaluated with the empirical relations proposed by [START_REF] Signell | Effect of wave-current interaction on wind-driven circulation in narrow, shallow embayments[END_REF] and U ω is the wave bottom orbital velocity issued from the wave propagation module. u * c is the shear velocity arising from the current alone and computed assuming a vertical logarithmic profile with (i) the value of the current at the first vertical σ-grid cell above the bottom and (ii) z 0b,ω .

Surface boundary conditions of temperature assume that the solar radiation Q sol is absorbed in the upper parts of the water column. At the sea surface, the infra-red and short-wave components of solar irradiance are thus equal taking the value of the solar radiation. Q sol is computed following [START_REF] Rosati | A general circulation model for upper ocean simulation[END_REF] and [START_REF] Luyten | COHERENS: A COupled Hydrodynamics-Ecological model for REgioNal and Shelf seas -Model Description (Available on CD-ROM[END_REF] using the correction of clear-sky value derived by [START_REF] Reed | On estimating insolation over the ocean[END_REF] to account for the cloud coverage and for the reflection by the ocean surface. Non-solar contributions Q nsol of (i) latent and (ii) sensible heat fluxes and (iii) net long-wave radiation are computed following [START_REF] Gill | Atmosphere-Ocean Dynamics[END_REF] and [START_REF] Luyten | COHERENS: A COupled Hydrodynamics-Ecological model for REgioNal and Shelf seas -Model Description (Available on CD-ROM[END_REF]. Formulations of solar and non-solar heat fluxes involve the 10-m wind components, air temperature, relative humidity and fractional cloud cover. The surface salinity flux is determined using the formula proposed by [START_REF] Steinhorn | Salt flux and evaporation[END_REF] involving the precipitation rate. Finally, the bottom boundary conditions for temperature and salinity are obtained by considering a zero flux normal to the seabed.

The set of equations is expressed in a spherical-σ coordinate system. Further details about the circulation module are given by [START_REF] Luyten | COHERENS: A COupled Hydrodynamics-Ecological model for REgioNal and Shelf seas -Model Description (Available on CD-ROM[END_REF] and [START_REF] Guillou | Rôles de l'hétérogénéité des sédiments de fond et des interactions houle-courant sur l'hydrodynamique et la dynamique sédimentaire en zone subtidale -applications en Manche orientale et la pointe de la Bretagne[END_REF].

Numerical methods

The wave spectral action balance equation is solved on a regular staggered grid, a constant directional resolution and an exponential frequency distribution with an implicit time discretization Euler technique. Further details about the boundary conditions and the numerical schemes are available in SWAN technical documentation (SWAN team, 2009). COHERENS circulation and transport equations are solved on a regular staggered grid with numerical schemes for time and space discretizations issued from the standard version of the code [START_REF] Luyten | COHERENS: A COupled Hydrodynamics-Ecological model for REgioNal and Shelf seas -Model Description (Available on CD-ROM[END_REF]. Two main modifications have been implemented. The first modification is associated with forcings of free surface and currents at the open boundaries. Mean velocities are imposed with an iterative scheme which minimizes wave reflection [START_REF] Flather | A tidal model of the northwest european continental shelf[END_REF]. The three-dimensional velocities normal to the open boundaries are imposed with the help of a simple radiation condition [START_REF] Blumberg | A description of a three-dimensional coastal ocean circulation model[END_REF]. Further details on this modification are available in [START_REF] Guillou | Rôles de l'hétérogénéité des sédiments de fond et des interactions houle-courant sur l'hydrodynamique et la dynamique sédimentaire en zone subtidale -applications en Manche orientale et la pointe de la Bretagne[END_REF] and [START_REF] Guillou | Three-dimensional modelling of tide-induced suspended transport of seabed multicomponent sediments in the eastern English Channel[END_REF]. The second modification deals with the computations of sea-surface and bottom roughnesses (section 2.2.2). An iterative procedure is implemented to ensure the convergence of sea-surface roughness predictions in Eqs. 1 to 3. Computation of apparent bottom roughness z 0,bω is realised on the basis of the following scheme. u * ω is first computed with waves parameters issued from SWAN. u * c is then obtained with the estimation of z 0,bω at the previous time step. Finally values of u * cω and z 0b,ω are determined using Eqs. 5 and 4, respectively.

Model setup

The geographical domain for full computation of hydrodynamics and transport equations extends in longitude from 6 o 000 W to 4 o 172 W and in latitude from 47 o 670 N to 48 o 822 N (Fig. 1). It is discretized on a 124 × 129 horizontal grid with a spacing of 1 km.

SWAN is set up on this computational domain adopting the parameterization of [START_REF] Guillou | Modelling impact of northerly wind-generated waves on sediments resuspensions in the Dover Strait and adjacent waters[END_REF] in the eastern English Channel. The wave propagation module runs with 30 exponentially spaced frequencies ranging from 0.05 Hz to 1 Hz, 60 evenly spaced directions (6 o resolution) and a time step of 5 min. The bottom friction coefficient is set to C JON = 0.038 m 2 s -3 [START_REF] Bouws | On the balance between growth and dissipation in an extreme, depthlimited wind-sea in the southern North Sea[END_REF]. Wind velocity components at 10 m above the free surface are provided by the meteorological model ALADIN ("Aire Limitée, Adaptation dynamique, Développement InterNational", Bénard, 2004, Météo-France). The wave module is driven by global WaveWatch III (WWIII) predictions of the National Oceanic and Atmospheric Administration (NOAA) (http://polar.ncep.noaa.gov/waves). ALADIN surface and WWIII lateral boundary conditions given every three hours are interpolated at all grid points and every computational time steps. SWAN is run over the years 2010 and 2011 to extend the comparison of numerical results with measurements at offshore station WB2 (section 2.1.1).

COHERENS is implemented on the same domain with 10-σ vertical-grid cells refined near the bottom and the surface. The time steps for external barotropic and internal baroclinic modes are 10 s and 100 s, respectively. The bottom roughness associated with the seabed is determined on the basis of maps established by sedimentologists in the nearshore areas of the Sea of Iroise over computational domain # 2 (e.g., [START_REF] Hinschberger | Carte sédimentologique sousmarine des côtes de France[END_REF][START_REF] Chassé | Atlas des fondes meubles du plateau continental du Golfe de Gascogne[END_REF]SHOM, 1996) (Fig. 2). Values are imposed according to observations for different bottom types compiled by [START_REF] Soulsby | The bottom boundary layer of shelf seas[END_REF]. The bottom roughness parameter is thus set to z 0 = 0.2 mm over mud deposits and z 0 = 0.4 mm over sand deposits in the bays of Douarnenez, Brest and Audierne as well as in the south-western areas which extends from the offshore boundary till the coastline in the north of Le Conquet. The roughness parameter takes the value of z 0 = 3 mm in regions of gravel and z 0 = 3.5 mm over rocky outcrops located in the north of computational domain #2, off the Crozon peninsula and in the north-western part of the bay of Audierne till the isle of Sein. The offshore bottom roughness is set to an uniform value of z 0 = 3.5 mm as implemented by [START_REF] Muller | High-resolution atmospheric forcing for regional oceanic model: the Iroise Sea[END_REF]. The circulation module is driven by free-surface elevation and depth-averaged currents predicted by the operational Iberian Biscay Irish (IBI) Ocean Analysis and Forecasting system and delivered at one-hour interval and a 3 km-spatial resolution by MyOcean project (http://www.myocean.eu). Benefits of using IBI hydrodynamic boundary conditions are the integration of surges and geostrophic velocities in addition to tide effects. Outflows at the mouth of rivers Elorn and Aulne in the bay of Brest (Fig. 1) are derived from measurements at two upstream stations (http://www.hydro.eaufrance.fr). Finally, ALADIN surface data of wind speed and atmospheric pressure and SWAN outputs are imposed at three-hours intervals in the circulation module.

IBI forecasts are also used to provide daily-averaged vertical profiles of temperature and salinity along maritime open boundaries. Surface heat fluxes are computed with parameters of 10-m wind components, air temperature, relative humidity and fractional cloud coverage given at three-hours intervals by ALADIN meteorological model. The precipitation rate is taken spatially-uniform and obtained from the database of the National Centers for Environmental Predictions (NCEP) (http://www.esrl.noaa.gov/ psd/data). Temperature boundary conditions at the rivers mouth are supplied by measurements at water treatment stations.

COHERENS is run over the period from April to October 2011 as IBI data were provided since April 2011 by MyOcean project and SIRANO observations were available till October 2011 (section 2.1.1). In order to investigate the effects of bottom roughness on SST predictions, three numerical experiments are conducted considering successively (i) an uniform bottom roughness parameter taken equal to z 0 = 0.0035 m as integrated by [START_REF] Muller | High-resolution atmospheric forcing for regional oceanic model: the Iroise Sea[END_REF] (experiment A), and the heterogeneous roughnesses associated with (ii) the granulometric distribution of seabed sediments displayed in Fig. 2 (experiment B) and (iii) the superimposed effect of the wave in the bottom boundary layer (experiment C) (Table 2). The three numerical experiments are compared with the standard statistical parameters of the maximum difference and the average of the absolute differences MABS of the SST given by the following relationship

MABS = 1 N i=N i=1 MABS i (6) with MABS i = |T α i -T β i | (7)
where T α i and T β i represent the two sets of measured or simulated SST data α and β for i ∈ [1, N ]. N refers alternately to the number of data in computational domain or in time series whether the analysis focuses on the spatial or temporal variabilities of numerical predictions.

Results and discussion

Comparison with observations

In-situ measurements

Predicted time series of wave height, peak period and peak direction are consistent with available measurements at station WB1 from January 2010 to September 2011 and station WB2 from January 2010 to November 2010. A close investigation is conducted on the comparison with measurements at station WB1 as observations were available at this point during the period of interest from April to September 2011 (Fig. 3). In spite of a slight overestimation around 5 -10 % of the significant wave height, the model reproduces fairly well the magnitude of the storms heights reaching values over 4 m in May, June and July 2011. The numerical results approach also the observed variations of the wave peak period and direction.

The comparison of SST numerical results and in-situ measurements is conducted on the basis of predictions for the most complete simulation titled experiment C (Table 2). Predictions are in agreement with observations along the averaged SIRANO vessel path from April to October 2011 (Fig. 4). The model reproduces the observed seasonal evolution of SST with increases in summer by 2 o C of offshore waters around the isles of Ushant and Molène (points #1 to #3) reaching 3 o C in nearshore waters (points #4 and #5) and 5 o C at the entrance of the bay of Brest (point #6). Whereas predictions tend to underestimate by 0.5-1 o C measurements in spring and autumn, differences are lessening in summer at points #1 to #5. Numerical results tend, however, to overestimate SST at point #6. This tendency is particularly noticeable in July and August 2011 when the maximum difference is reaching 1.5 o C. Whereas the 1 km-spatial resolution may be too large for a precise approach of water mass and temperature exchanges between the bay of Brest and the Sea of Iroise, the present configuration approaches the main offshore SST patterns while avoiding prohibitive demand on computer computational time and memory. Numerical predictions reproduces thus fairly well the daily and bi-monthly SST variations exhibited at fixed-point stations WB1 and WB2 from April to September 2011 (Fig. 5). Daily changes in SST characterized the night-day cycle. Bi-monthly variations appear to result from the strength of the tide with reduced SST during spring and increased SST during neap tidal cycles (Fig. 6). These results confirm the well-known significance of the tide on temperature vertical mixing in the Sea of Iroise (e.g., [START_REF] Altazin-Pichon | Application d'un modèle de thermocline à la formation du front thermique en mer d'Iroise. Confrontation des résultats avec des mesures in situ[END_REF]Mariette et al., 1982;[START_REF] Mariette | Effet des échanges atmosphériques sur la structure thermique marine. Application à des zones du large et à une zone côtière[END_REF][START_REF] Mariette | Simulation of the formation of Ushant thermal front[END_REF]. These SST variations are however difficult to capture with SIRANO observations in relation to the weak number of data per day (section 2.1.1).

Satellite images

SST time series derived from remote-sensing data are consistent with in-situ measurements at nearshore (Fig. 4) and offshore (Fig. 5) locations in spite of a slight underestimation of observed values by 0.5 o C in spring and autumn. These comparisons show the benefit of extending the analysis of numerical prediction through a confrontation with satellite images. An overall good agreement is obtained between observations and predictions of SST spatial patterns during the period of interest, from April to October 2011 (Fig. 7). In spring (Fig. 7-a), the modelling system reproduces fairly well the warming of surface waters along the southern boundary where tidal currents and associated mixing are too weak to stand in the way of vertical stratification [START_REF] Cann | Evolution annuelle de la structure hydrologique du plateau continental au Sud de la Bretagne[END_REF]. Numerical results approach also the warming of surface waters in the nearshore areas of the bay of Douarnenez where remote sensing data are available. In summer (Fig. 7-b), predictions exhibit clearly the development of a region of intense vertical mixing from the northern boundary till the south-western extend of the reef of Sein. This area characterized by weak SST below 14 o C has been identified by numerous scientific studies (e.g., [START_REF] Pingree | Survival of dinoflagellate blooms in the western English Channel[END_REF][START_REF] Mariette | Simulation of the formation of Ushant thermal front[END_REF][START_REF] Boyer | Observations of the Ushant tidal front in September 2007[END_REF]. This thermal structure is associated with the development of two horizontal thermal fronts, (i) the former, denoted the Ushant front, appearing a few kilometres off the isle of Ushant till the reef of Sein [START_REF] Pingree | Survival of dinoflagellate blooms in the western English Channel[END_REF][START_REF] Mariette | Le front thermique d'Ouessant en août et septembre 1982, campagne Satir Dynatlant. Campagne océanographique française[END_REF], (ii) the latter, creating at the verge of the system made by the bays of Douarnenez and Brest (e.g., [START_REF] Muller | High-resolution atmospheric forcing for regional oceanic model: the Iroise Sea[END_REF]. The modelling system approaches fairly well the associated horizontal thermal gradient of around 4 o C in less than 2 km. Nevertheless, SST tends to be overestimated in the nearshore areas of the bays of Brest and Douarnenez, as well as in the intermediate region between the two cold predicted areas around the isle of Ushant and near the reef of Sein. These differences may be associated with the difficulty to represent vertical mixing in most ocean circulation models in relation to parameterizations of turbulence closure schemes and surface roughness [START_REF] Lopes | Modelling the temperature and the phytoplankton distributions at the Aveiro near coastal zone, Portugal[END_REF]Renaudie et al., 2011). These differences attributed to underestimated vertical mixings are however lessening in autumn (Fig. 7-c). SST is thus found to be overestimated by 0.5 -1 o C over these areas in 28 September 2011. The global comparison with satellite images confirms the capability of the model predictions to reproduce the major SST patterns appearing from spring till autumn 2011 in the Sea of Iroise.

Sensitivity study

Improvements of numerical predictions

The improvement of SST predictions reached with the three parameterizations of bottom roughness (Table 2) is analysed further. This investigation relies on SST derived from satellite images as slight differences are obtained between the three numerical experiments A, B and C at each measuring points #1 to #6 and WB1 and WB2. Although remote-sensing data may present biases, this analysis gives a preliminary estimation of the effects of bottom roughness on predicted SST. The comparison is conducted retaining satellite observations with more than 70 % of available data in computational domain #2 (Fig. 8-a). Numerical predictions are interpolated on the grid of remote-sensing data over the simulation domain. Finally, the average of the absolute differences between predicted and observed SST is computed for each day retained resulting in three values of MABS (Eq. 6): MABS A , MABS B and MABS C for configurations A, B and C, respectively. Fig. 8-b displays the differences MABS A -MABS B over the period April-October 2011. Positive values in Fig. 8-b show the improvement obtained in the estimation of SST derived from satellite images by integrating a heterogeneous bottom roughness distribution associated with the granulometric distribution of seabed sediments. The bottom roughness parameterization is found to have an impact on SST numerical estimates in the nearshore areas of the Sea of Iroise for the period of simulation. The implementation of a semi-realistic heterogeneous-seabed roughness is thus improving globally SST predictions in spite of local increased differences in summer and autumn.

Differences are exhibited with the superimposed effect of waves in the bottom boundary layer. Fig. 8-c shows the differences MABS A -MABS C over the period of interest. Increase of the apparent bottom roughness has a non-negligible effect on SST numerical estimates highlighting differences during storm events of May, July and September 2011. The combined integration of an heterogeneous seabed roughness and waves in the bottom [START_REF] Soulsby | Wave-current interaction within and outside the bottom boundary layer[END_REF][START_REF] Zhang | Hydrodynamic model with wave-current interaction in coastal regions[END_REF]. In the present investigation, the formulations here retained are considered to approach the overall effect of waves roughness on SST in the Sea of Iroise.

Satellite

SST spatial and temporal variabilities

Numerical predictions are exploited further to analyse the variability of SST in computational domain #2 where the heterogeneous bottom roughness parameterizations are introduced. The investigation is conducted over the period July-September 2011 when horizontal thermal gradients are well developed (e.g., [START_REF] Boyer | Observations of the Ushant tidal front in September 2007[END_REF]. Figs. 9-A1 and 9-A2 display the maximum differences and the average of the absolute differences between SST predicted with configurations B and A. These results confirm the negligible influence of the seabed roughness distribution on SST predicted along the route of the vessel path. The maximum difference lies below 0.2 o C for the period considered in this area (Fig. 9-A1). Main differences are obtained offshore at the north-western and south-western edges of the external thermal front of Ushant with maximum SST changes over 1 o C. Indeed, these two offshore regions are found to be the most sensible to the bottom roughness parameterization as being characterized by significant tidal hydrodynamic regimes (e.g., SHOM, 1968) and partially-mixed vertical-temperature profiles. Secondary differences are obtained nearshore (i) in the south of the bay of Douarnenez and (ii) in the south-eastern part of the bay of Brest. Both regions are characterized by strong-predicted horizontal-thermal gradients (Fig. 7). The region identified in the bay of Douarnenez is thus located at the interface between warm coastal and cold offshore surface waters. The superimposed effect of waves on predicted SST is displayed in Figs. 9-B1 and 9-B2 with the maximum differences and the average of the absolute differences between SST predicted with configurations C and A. Waves appear to have an impact on SST (i) in the bay of Audierne and (ii) off the southern part of Crozon peninsula with maximum differences in predicted SST over 1 o C. The averaged difference reaches also its maximum value of 0.2 o C off Crozon peninsula. These results are explained by the significant exposure of these two regions to the incident waves in the Sea of Iroise. Waves are thus appearing to modulate the SST in the intermediate thermal region located between the two cold predicted areas around the isle of Ushant and the reef of Sein.

The temporal variability of predicted SST is analysed further off Crozon peninsula at location t 1 (Fig. 9-B1, λ = 4.60 o W, φ = 48.20 o N) where the effects of waves on simulations have been exhibited. The local evolution of predicted SST presents major changes in conditions of combined (i) spring-tide and moderate waves and (ii) storm waves . Predictions are slightly influenced by the integration of the heterogeneous bottom roughness associated the grain-size of seabed sediments. Nevertheless, the superimposed effect of waves is found to increase SST by more than 1 o C during spring-tide conditions of mid-August 2011. This analysis is extended by averaging the differences over computational domain #2. Fig 11-b displays the time series of the average of the absolute differences between SST predicted with configurations B and A. This evolution t 1 Figure 9: Maximum differences and average of the absolute differences between SST predicted with configurations (A1-A2) B and A and (B1-B2) C and A from July to September 2011. The black square in Fig. B1 shows the location where the SST evolution is analysed further in Fig. 10.

of the averaged difference is characterized by spring-neap tide modulations with maximum values obtained during spring tides. The significance of the tide on temperature gradients in the Sea of Iroise (section 3.1.1) explains these modulations. Indeed, changes in bottom roughness modify the bottom friction associated with the tide thus impacting the vertical mixing of temperature and the resulting SST. This effect is stronger for strong bottom constraints obtained during spring tides. Differences are naturally exhibited for highest horizontal thermal gradients developing in spring and summer in the Sea of Iroise (June, July and August 2011). The superimposed effect of the waves in the bottom boundary layer globally increases these differences as the apparent bottom roughness is increasing. The time series of the average of the absolute differences in computational domain #2 between predictions issued from configurations C and A is still characterized by spring-neap tide modulations. This periodicity tends however to lessen during highest storm events of early May and June, mid-July and September 2011.

Conclusions

A 3D hydrological model based on the coupling of COHERENS circulation and SWAN wave propagation modules has been implemented in the Sea of Iroise to investigate the effects of the heterogeneous seabed roughness and the wave in the bottom boundary layer on SST predictions. Numerical results have been compared with in-situ measurements at fixed-point stations and along the route of a vessel travelling between the coast and the isle of Ushant. This comparison has been extended to SST derived from satellite images. The main outcomes of the present study are the following.

(1) Numerical predictions reproduce the observed seasonal, spring-neap tide and daynight evolutions of SST in the nearshore areas of the computational domain as well as major spatial SST patterns characterizing the evolution of thermal gradients in the Sea of Iroise. Theses comparisons confirm the significance of the tide in the development of horizontal thermal gradients and vertical stratification in the nearshore areas.

(2) The sensitivity study exhibits the effect of bottom roughness parameterizations on SST predictions. The integration of a heterogeneous bottom roughness distribution is found to improve slightly the numerical estimates of SST. These results are not so well established with the superimposed effect of the waves on the bottom roughness. Nevertheless, its integration is also leading to global improvements of numerical predictions.

(3) The consequences of these parameterizations on spatial and temporal variabilities of predicted SST are analysed further. Mappings of the differences in SST predicted with the different formulations are produced in the nearshore areas of the Sea of Iroise. Sensitivity of numerical predictions is noticeably exacerbated in regions of high thermal gradients. While the heterogeneous bottom roughness distribution is found to have a major impact at the edge of the Ushant thermal front, waves appear to increase mixing of temperature in the nearshore areas of the bay of Audierne and the western extend of Crozon peninsula.

The present study provides thus interesting insights into the evolution of SST in the nearshore areas of the Sea of Iroise. Available in-situ measurements sites appear however to be minimally impacted by the different parameterizations of bottom roughness implemented. A prospective of this research will consist in refining the comparison with complementary SST observations realized in the bay of Audierne and in the intermediate area of horizontal thermal gradients off Crozon peninsula. These results promote the integration of an heterogeneous bottom roughness distribution over the whole computational domain relying on complementary observations of bottom substrate. Furthermore, the comparison could be extended to additional observed parameters derived from SIRANO project like the surface salinity, turbidity or chlorophyll-a fluorescence. These developments will aim at an improved numerical hydrological application of high concerns for water quality purposes in the Sea of Iroise.

Aknowledgments

The authors are grateful to the MyOcean (European Commission) project for providing numerical predictions of the operational Iberian Biscay Irish Ocean Analysis and Forecasting system and remote sensing observations of SST derived from the European Ocean-Sea Surface Temperature MultiSensor L3. Météo-France supplied measurements of wave parameters and SST at offshore stations as well as wind fields and surface heat fluxes obtained with the meteorological model ALADIN. The authors warmly thank "le conseil général du Finistère" and "Brest Métropole Océane" for the financial support of the SIRANO project, as well as the shipping company "Penn ar Bed" for providing access aboard "Enez Eussa III" vessel. Simulations were performed on computer facilities CAPARMOR ("CAlcul PARallèle Mutualisé pour l'Océanographie et la Recherche"). The present paper is a contribution to the research program of the Laboratory of Coastal Engineering and Environment (http://memphys-lgce.fr.ht).

Figure 1 :

 1 Figure 1: Bathymetry and computational domain #1. Red squares show locations selected for the extraction of SST time series along the averaged vessel path displayed by the green line. Red triangles indicate the positions of the available offshore wave buoys WB1 and WB2. The left-bottom inset displays the position of the computational domain #1 in the North-East European continental shelf.

  mm

Figure 2 :

 2 Figure 2: Spatial heterogeneous bottom roughness parameter associated with the granulometric distribution of seabed sediments in computational domain #2.

Figure 3 :

 3 Figure 3: Measured (black line) and computed (blue line) time series of (a) the significant wave height, (b) the peak period and (c) the peak direction (anticlockwise from the East) at station WB1 from April to October 2011.

Figure 4 :WB2Figure 5 :FreeFigure 6 :

 456 Figure 4: Measured (red lines) and computed from experiment C (blue lines) time series of SST at points #1 to #6. Green circles show SST at points #1 to #3 derived from satellite observations.

Figure 7 :

 7 Figure 7: Observed (left) and computed from experiment C (right) SST on (a) 25 May, (b) 30 August and (c) 28 September 2011. Clouds (blank data) appear as white patches on remote sensing images.

Figure 8 :

 8 Figure 8: (a) Index coverage of SST satellite data in computational domain #2. Days when the index coverage is over 70 % are displayed with light-grey bars. Days selected in Fig. 7 are showed with black bars. (b and c) Differences in the averaged absolute estimation of SST observed by satellite between configurations (a) B and A and (b) C and A. Positive values indicate an improved estimation of SST with simulations (a) B and (b) C, respectively.

Figure 10 :Figure 11 :

 1011 Figure 10: Time series of (a) the SST predicted from configurations B (blue line) and C (red line) and (b) the differences between SST predicted from configurations B and A (blue line) and C and A (red line) at location t1.

Table 2 :

 2 List of numerical experiments for the circulation and transport modules COHERENS.