Stefanie Rach
email: stefanie.rach@ovgu.de

Stefan Ufer
email: ufer@math.lmu.de

Timo Kosiol
email: kosiol@math.lmu.de

Self-concept in university mathematics courses

Keywords: Mathematical self-concept, Transition school-university, Mathematical practices, Learning prerequisite

Many researchers agree that mathematical self-concept is an important factor in (university) learning processes. Mathematics learning at university differs substantially from learning mathematics at school. Especially the character of the learning domain mathematics changes at the transition to university. In this contribution, we present newly developed instruments for selfconcept that take the specific character of mathematics at university into account. We applied the instruments in a first-semester course with 344 students. The results of exploratory factor and correlation analyses indicates that it is possible to differentiate facets of self-concept according to different characters of the learning domain mathematics. Finally, we discuss how precise information concerning learners' self-concept can promote to support students at this challenging transition to university.

Introduction

There is no doubt that affective variables are important factors in successful, mathematical learning processes [START_REF] Hannula | The structure and dynamics of affect in mathematical thinking and learning[END_REF]. In this contribution, we concentrate on self-concept concerning mathematics. In a recent study, self-concept was identified as an essential learning prerequisite to predict achievement in school mathematics [START_REF] Feng | Akademische Selbstkonzepte und akademische Selbstwirksamkeiten: Interdependenzen und Beziehungen zu schulischen Leistungen [Academic self-concepts and self-efficacies: interdependencies and relations to preformances in school[END_REF]. Moreover, self-concept substantially mediates the relation between achievement and emotions (Van der Breek, [START_REF] Van Der Breek | Self-concept mediates the relation between achievement and emotions in mathematics[END_REF]. Many existing studies deal with the role of self-concept in mathematical teaching and learning processes at school. In contrast, only few studies analyze its role in learning processes at university. As learning processes in these two institutions differ significantly from each other, we claim the need for specific research on the role of self-concept in mathematics courses at university and in particular during the transition to university mathematics.

Questionnaires are the most common instruments to survey mathematical self-concept. The learning domain, for which self-concept should be reported, is mostly broadly described using the word "mathematics". At the transition from school to university, however, it is not clear if students refer to school or to university mathematics when reporting their self-concept. To obtain a more differentiated insight into students' self-concept, we developed questionnaires for mathematical self-concept that take the specific learning domain at university into account. In this contribution, we present the conceptualization of these instruments in detail. In a study with 344 first-semester students, we studied if the assumed facets of self-concept can be measured and differentiated empirically.

The role of self-concept in mathematical learning processes

Self-concept, self-efficacy, and self-esteem are important constructs which describe students' views about themselves. The source of students' views about themselves are often experiences of past success or failure. As self-esteem has a focus on emotions and is not as prominent as the other two constructs in analyzing subject-specific learning processes, we concentrate on the constructs selfconcept and self-efficacy. Self-concept has its focus on the persons' skills and abilities, whereas self-efficacy refers to one's beliefs to successfully perform a certain action in the future [START_REF] Marsh | The Murky Distinction Between Self-Concept and Self-Efficacy -Beware of Lurking Jingle-Jangle Fallacies[END_REF]. Researchers use both concepts to explain and predict learners' action and success [START_REF] Bong | Academic Self-Concept and Self-Efficacy: How Different Are They Really[END_REF]. As we are interested in students' views of themselves as learners in mathematics at the period of transition, we also want to analyze the sources of students' beliefs about their own mathematical knowledge and skills. That is why we use the construct self-concept. We refer to "mathematical self-concept (of ability)" as students' beliefs about their own mathematical knowledge and skills. Theoretically, self-concept is often placed between motivational and cognitive variables, since it is built on views (affect side) which refer to knowledge and skills (cognition side).

One mechanism leading to the relationship between self-concept and achievement might be that learners with a strong self-concept choose to engage in more demanding tasks, which results in better learning and higher achievement. Moreover, there is much evidence that underpins the relation between self-concept and other motivational variables, like interest [START_REF] Cai | Direct and indirect effects of self-concept of ability on math skills[END_REF][START_REF] Rach | The transition from school to university in mathematics: Which influence do school-related variables have?[END_REF]. It is assumed that self-concept mediates the relation between achievement and emotions [START_REF] Van Der Breek | Self-concept mediates the relation between achievement and emotions in mathematics[END_REF]. In university contexts, explorative studies claim that a low self-concept and the decrease of self-concept in the first study year even of students with excellent learning prerequisites probably lead to dropout [START_REF] Bampili | The transition from high school to university mathematics: a multidimensional process[END_REF][START_REF] Martino | The mathematical crisis in secondary-tertiary transition[END_REF].

However, the studies mentioned above mainly relate to the school context (e.g. [START_REF] Cai | Direct and indirect effects of self-concept of ability on math skills[END_REF]. Analyses of learning processes at university often show only weak or non-significant relations between self-efficacy respectively self-concept and study success [START_REF] Bengmark | Success-factors in transition to university mathematics[END_REF][START_REF] Rach | The transition from school to university in mathematics: Which influence do school-related variables have?[END_REF]. One reason for this unexpected result might lie in the differences of the learning domain between school and university. When students rate their mathematical self-concept in the first semester at university, they might refer to their beliefs about their knowledge and skills according to mathematics as a school subject, which could be less relevant for learning in this context than self-concept regarding university mathematics.

Teaching and learning mathematics at university

In Germany, as in many other countries all over the world (e.g. South Africa: [START_REF] Engelbrecht | Adding structure to the transition process to advanced mathematical activity[END_REF]France: Gueudet, 2008), there seems to be a substantial gap between school and university concerning teaching and learning of mathematics. Not only the social contexts (e.g. the peer group) and the learning opportunities and their use (e.g. from a more guided form in school to a more selfregulated form at university) change at this institutional transition, but also the learning domain itself. At school, one important goal of teaching and learning mathematics is to apply mathematics for solving real-world problems. Thus, classrooms instruction focuses on describing situations mathematically and performing calculations. We call this special character of mathematics "school mathematics". In contrast to that, "university mathematics" denotes the character of mathematics presented in mathematics university courses, which refer to mathematics as a scientific discipline that is built on formal definitions of concepts and deductive proofs [START_REF] Engelbrecht | Adding structure to the transition process to advanced mathematical activity[END_REF]. Central practices in the first year of studying mathematics at university include dealing with formal presentations of concepts and proving statements. As demands of proving tasks are mainly high and unfamiliar to freshmen at university, students often struggle in their first year of university and a substantial share of them drop out from their study program [START_REF] Heublein | Die Entwicklung der Studienabbruchquoten an den deutschen Hochschulen[END_REF].

Summarizing, the learning subject changes at the transition from school to university from a school subject focusing on applications to a scientific discipline focusing on the structure of a mathematical theory. That is why instruments which measure mathematical self-concept in a generic way and results concerning the role of mathematical self-concept in learning processes at school might not be transferable to processes at university.

The current study

As part of the project SISMa ("Self-concept and Interest when Studying Mathematics"), it is the goal of this study to differentiate self-concept concerning different characters of the learning domain mathematics. The aim of the project is to clarify the role of affect in mathematical learning processes during the transition to university mathematics (see [START_REF] Ufer | Interest in mathematics = interest in mathematics? What general measures of interest reflect when the object of interest changes[END_REF]. In this contribution, we focus on mathematical self-concept and present instruments that measure different facets of self-concept according to different characters of mathematics (Table 1, see also [START_REF] Schukajlow | Teaching methods for modelling problems and students' task-specific enjoyment, value, interest and selfefficacy expectations[END_REF] for a similar approach concerning selfefficacy; see also [START_REF] Ufer | Interest in mathematics = interest in mathematics? What general measures of interest reflect when the object of interest changes[END_REF] for the construct interest). To measure the different facets of selfconcept we constructed two types of scales: The first type of self-concept scales surveys beliefs about knowledge and skills regarding mathematics as it has been experienced respectively anticipated in a specific context. These statements directly address one of the two institutions, in which mathematics is taught and learnt: school versus university. The second type of scales addresses self-concept regarding mathematical practices, which are characteristic for school mathematics (applying mathematics), for university mathematics (proving and dealing with formal representations), or for both contexts (using mathematical calculation techniques). These five scales were developed based on prominent models of self-concept taking into account different frames of reference [START_REF] Bong | Academic Self-Concept and Self-Efficacy: How Different Are They Really[END_REF]. In contrast to other scales, e.g. [START_REF] Kauper | PaLea -Panel zum Lehramtsstudium [PaLea -Panel to teacher education programs[END_REF], different aspects of mathematics as points of reference for individual beliefs are specified.

To study whether these facets of self-concept can be differentiated empirically, we conduct a study with first-year mathematics students. The following questions deal with the structure of the questionnaires and the relation of the self-concept measures to other learning prerequisites:

1) Is the theoretical structure of the subscales reflected in the factorial structure of the newly developed instruments?

We expected that factor analyses would underpin the theoretical conceptualization of the subscales. Moreover, we expected self-concept in applying mathematics to be primarily correlated to self-concept concerning school mathematics and self-concept concerning proving and dealing with formal representations to be primarily related to self-concept concerning university mathematics.

2) Are the different facets of self-concept related to other learning prerequisites?

We expected that self-concept concerning school mathematics relate to interest concerning school mathematics, the same pattern with university mathematics. In line with previous research (e.g., [START_REF] Cai | Direct and indirect effects of self-concept of ability on math skills[END_REF], we expected a relationship between self-concept measures and mathematical knowledge respectively the school qualification grade.

3) Is there a relation between facets of self-concept and study choice?

As a mathematics teacher education program is not as much focused on mathematics as a mathematics bachelor program, we expected that, on average, students with lower mathematical self-concept concerning university mathematics respectively self-concept concerning proving and dealing with formal representations would be more likely to choose a teacher education program. This should result in lower average self-concept concerning university mathematics respectively proving and dealing with formal representations of the teacher education students than of mathematics bachelor students. We had no specific hypotheses regarding self-concept concerning school mathematics respectively concerning applying mathematics and using calculation techniques.

Method

The sample of this study comprised 344 first-semester-students of the mathematics courses "Analysis I" from one university in the southern part of Germany. In this course, mathematics is presented as a scientific discipline with a focus on formal concept definitions and deductive proofs.

We use a complete survey of all students who start their study in a teacher education program or in a mathematics respectively business mathematics bachelor program. As the study took place in the first lecture of the first-semester mathematics courses "Analysis I" and students participated in the survey voluntarily, we can't say anything about students who did not participate in the study. Most of the participating students were in a teacher education program for two secondary school tracks (Realschule, Gymnasium) in Germany, N = 130, and in a mathematics respectively business mathematics bachelor program, N = 184.

Self-concept scale Sample item M (SD) Cron-bach´s α

General I am very good in mathematics. (4 items) 2.07 (.50) .76

Institution

School mathematics

The mathematics that I know from school is easy for me. (3 items)

(.57)

.73

University mathematics

The mathematics that is done at university is easy for me. (3 items) 1.51 (.65) .84

Practice

Applying mathematics

Applying mathematics to real-world problems is not so easy for me. (reversed item) (5 items) 2.00 (.51) .80 We used a general scale for mathematical self-concept [START_REF] Kauper | PaLea -Panel zum Lehramtsstudium [PaLea -Panel to teacher education programs[END_REF], for sample items see Table 1) to compare our newly developed instruments with an approved scale. Moreover, we applied the new self-concept scales as differentiated measures of self-concept (see Table 1). The participants were asked to assess all mixed statements on a four-point Likert scale from 0 (disagree) to 3 (agree). The individual mean value of a single student on a scale was computed if this student had answered at least half of the items of the scale. We assessed additional affective and cognitive variables in the first lecture: the school qualification grade (grades were recoded so that 4.0 is the best and 1.0 is the worst value), prior knowledge for advanced mathematics, and interest in school mathematics respectively university mathematics (see [START_REF] Ufer | Interest in mathematics = interest in mathematics? What general measures of interest reflect when the object of interest changes[END_REF].

Proof and formal

Results

Differentiated measures of self-concept

Table 1 shows the mean values, standard deviations, and reliability coefficients of the self-concept scales. There are no floor or ceiling effects.

Two explanatory factor analyses (Principal Component Analysis with Varimax rotation)one for the three self-concept scales concerning practices and one for the two self-concept scales concerning the institutionsshowed three respectively two factors, that were in line with the theoretical structure of the instruments. Reliability analyses underpin the internal consistency of the general self-concept scale and the five newly developed scales, as all scales show a moderate to good consistency. Correlation analyses also partly promote the expected structure: For example, self-concept concerning proving and dealing with formal representations correlates with selfconcept concerning university mathematics strongly, r = .65 (Table 2). The lower correlation, r = .26 between self-concept concerning applying mathematics and self-concept concerning school mathematics was unexpected, because applying mathematics to real-world problems should be a prominent activity in mathematics classrooms. All specific facets of self-concept are correlated significantly and positively with the general measure. In sum, the different facets of self-concept can be separated empirically, and their correlational pattern reflects the assumed specific nature of university mathematics.

General

Differences between study programs and study choice

Table 4 shows mean values (and standard deviations) for students from the two programs on all facets of self-concepts. Group differences were tested for significance and we calculated effect sizes. As expected, students in the bachelor program show a moderately, but significantly higher selfconcept than teacher education students concerning university mathematics, and, though not significantly, also concerning proof and formal representations.

General

Discussion

While the prominent role of self-concept for successful learning processes at school is well established [START_REF] Cai | Direct and indirect effects of self-concept of ability on math skills[END_REF], its role in the university context is yet worthy of discussion. With this project, we shed light on the role of self-concept in the transition to university mathematics using differentiated measures of self-concept. Applying newly developed instruments, we distinguish different facets of self-concept of first-semester students and relate these facets to other learning prerequisites respectively the choice of the study program. The results on correlations and group differences provide first evidence that the scales do differentiate between the theoretically conceptualized facets of mathematical self-concept. However, qualifications are warranted for a broad application of the scale. For example, the results indicate that students seem to judge their knowledge and skills to apply mathematics to real-world problems not primarily based on their beliefs about their knowledge and skills regarding school or university mathematics. This might reflect that authentic applications are not considered specific to university mathematics, but also rare in German school classrooms [START_REF] Jordan | Aufgaben im COACTIV-Projekt [Tasks in the COACTIV-project[END_REF]. The small differences in self-concept between the two programs indicate that primarily self-concept regarding university mathematics is related to study choice. This facet of self-concept turned out to be related to prior mathematical knowledge, but not to the school qualification grade. It remains an open question, if the school qualification grade, which predicts success in the first semester above and beyond prior mathematical knowledge [START_REF] Rach | The transition from school to university in mathematics: Which influence do school-related variables have?[END_REF], has an influence on study choice that is not mediated by self-concept. Of course, the results of our study are based on students' self-reports about their self-concept. To get a clearer picture of the impact of self-concept in concrete learning processes, it seems worthwhile to combine our approach with analyzing students' reported experiences and their concrete learning behavior in the first year of study (e.g. di [START_REF] Martino | The mathematical crisis in secondary-tertiary transition[END_REF].

In sum, we presented the conceptualization of instruments to measure different facets of selfconcept concerning school respectively university mathematics and corresponding mathematical practices. Using these measures, it is possible in the future (1) to investigate the development of these variables during students' learning processes and their effect on students' learning activities in undergraduate mathematics programs, and most importantly their tendency to drop out of a study program.

(2) The differentiated measures may allow more differentiated insights into students' affect. This, in turn, may allow (3) to develop adequate approaches to support students during the challenging transition to a university mathematics program. One idea to support students is to adaptively select mathematical tasks in the courses that fit individual students' prior knowledge so that they can approach these tasks in a meaningful way. If students perceive competence [START_REF] Deci | Handbook of self-determination research[END_REF] when working on these tasks, this should probably lead to the development of selfconcept concerning university mathematics, for example mediated by intrinsic motivation (see [START_REF] Krapp | Basic needs and the development of interest and intrinsic motivational orientations[END_REF]. A higher self-concept, in turn, might lead to a better learning behavior, specifically to students choosing more demanding tasks and showing more perseverance when dealing with these tasks. All in all, such interventions aiming at a higher, yet realistic self-concept, are a promising approach to decrease the rate of students dropping out of mathematics study programs.

Table 1 : Measurement instruments for self-concept with means, standard deviations, and reliability coefficients, N = 252-333. Statements rated on a four-point Likert scale from 0 (disagree) to 3 (agree)

 1

	Understanding mathematical proofs is easy	1.73	.82

Table 2 : Correlations for the self-concept scales, ** p < .01 Connection to other learning prerequisites

 2 As expected, correlations of variables focusing the same character of mathematics, school respectively university mathematics, are stronger than correlations concerning variables on different characters of mathematics (Table3). Only self-concept concerning school mathematics correlates with the school qualification grade significantly. Both self-concept scales weakly relate to mathematical knowledge.

		Application	Calculation	Proof and	School	University
	(SCG)	(SCA)	(SCC)	Formal (SCP)	(SCS)	(SCU)
	SCG	.35**	.51**	.49**	.61**	.51**
	SCA		.31**	.35**	.26**	.27**
	SCC			.38**	.48**	.34**
	SCP				.29**	.65**

Table 3 : Correlations of the self-concept scales with other learning prerequisites, ** p < .01, * p < .05

 3

Table 4 : Mean values (standard deviation) and results of tests of group differences between study programs, * p < .05, t p < .10

 4

			Application Calculation	Proof and formal	School	University
	Mathematics bachelor program	2.13 (0.55)	2.00 (0.53)	1.88 (0.48)	1.80 (0.48)	2.36 (0.58)	1.61 (0.65)
	Teacher education program	2.07 (0.39)	2.03 (0.50)	1.99 (0.46)	1.71 (0.45)	2.40 (0.54)	1.42 (0.62)
	d	0.10	-0.05	-0.23 t	0.19	-0.06	0.29*


Marloes Van Hoeve
email: m.l.vanhoeve@uu.nl

Michiel Doorman
email: m.doorman@uu.nl

Michiel Veldhuis
email: m.veldhuis@uu.nl

How can teachers influence their students' (mathematical) mindset?

Keywords: Learning motivation, teacher influence, psychology

Interventions aimed at fostering students' growth mindsets have been carried out in 21 classrooms

(with a focus on Grade 7 and Grade 10) in the Netherlands. The intervention consisted of three main elements: introduction to neuroplasticity, the importance of learning from errors in learning processes, and growth-mindset feedback. Before and after the intervention, the students finished a questionnaire, and during the intervention, students and their teachers were interviewed. Results indicate that the students' mindsets tended to be more towards a growth mindset after the intervention, in particular for the Grade 10 students. Students were very positive about the intervention, especially the neuroplasticity and the attention for and learning from errors. Teachers and students valued the changes in attitudes and interactions with a new language for teaching and learning mathematics.

Introduction

"I don't understand anything" or "What a stupid mistake" are phrases students often say out loud. For teachers, when they pay attention, these words can be an important signal to indicate that students are working with a fixed mindset. Recognition of the mindset by the teacher and explanation of the theory of mindset can help students change their mindset, and by that change their beliefs and attitudes towards mathematics. To influence students' mindset the role of the teacher is indispensable.

Theory of the mindset

The concepts of fixed and growth mindset were introduced by Carol Dweck [START_REF] Dweck | Mindset, The new psychology of success[END_REF][START_REF] Dweck | Implicit theories and their role in judgement and reactions: a world from two perspectives[END_REF]. She distinguished, based on 20 years of research, two types of mindset:

• FIXED: you have certain talents, and they remain the same throughout your life.

• GROWTH: what you can do or learn now forms the starting point from which you can develop.

Their studies show that the effects of these different mindsets on how students learn are significant, especially in how they deal with challenges and obstacles. When students have a fixed mindset they prefer not to get any challenges. One might think: "Suppose I fail, then people will think I am not very clever, and as this cannot change, I will stay dumb for the rest of my life." If something goes wrong, and the students have a fixed mindset, then they will feel stuck in a situation to which they cannot change anything. On the other hand, when students are working with a growth mindset then they want challenges. The outcome does not really matter to them; they know and feel that it is important just to try, that they can learn from their mistakes, that their brains are at work, and that they can change [START_REF] Boaler | Mathematical mindset[END_REF][START_REF] Dweck | Mindset, The new psychology of success[END_REF].

The mindset students have is influenced by their upbringing. For example, parents who say "I was never able to do mathematics when I was young" unintentionally influence their children into a fixed mindset. The emphasis on performance in our school systems also plays an important role. High grades and quick results are seen as positive, while they can make students insecure and tend to create a fixed mindset [START_REF] Dweck | Implicit theories and their role in judgement and reactions: a world from two perspectives[END_REF][START_REF] Dweck | Mindset, The new psychology of success[END_REF][START_REF] Mueller | Praise for intelligence can undermine children's motivation and performance[END_REF]. A recent large scale study among undergraduate students showed that their teachers' mindset beliefs influenced classroom experiences and had a substantial effect on their achievements in STEM fields [START_REF] Canning | STEM faculty who believe ability is fixed have larger racial achievement gaps and inspire less student motivation in their classes[END_REF].

'Mindset' is not a trait and it cannot be measured exactly. A mindset may vary with context and over time [START_REF] Dweck | Mindset, The new psychology of success[END_REF]. However, one's mindset has an impact on how one approaches and becomes involved in an activity. When students behave according to a fixed mindset while encountering a problem, they are likely to give up quickly and tell themselves: "I will never learn this." In contrast, when students are working with a growth mindset, they ask themselves "what can I learn from this", and "how can I try not to make the same mistake too many times." [START_REF] Dweck | Mindset, The new psychology of success[END_REF]. For teachers, when they pay attention to the words of their students, these words can be an important signal to indicate that students are working with a fixed or growth mindset. Recognition of the mindset by the teacher and explanation of the theory of mindset can help students change their mindset, and by that change their beliefs and attitudes towards mathematics [START_REF] Boaler | Mathematical mindset[END_REF].

Interventions that encourage a growth mindset

For everybody, students and teachers, it is important to become aware of the impact of their mindset and of its possibilities and challenges [START_REF] Dweck | Mindset, The new psychology of success[END_REF]. With this awareness, in combination with relatively small social psychological interventions, it has been found that teachers can encourage students to adopt a growth mindset [START_REF] Yeager | Social-psychological interventions in education: they're not magic[END_REF].

If students believe that they can be smarter and that hard work can help them with this, then they are more willing to exercise [START_REF] Blackwell | Implicit theories of intelligence predict achievement across an adolescent transition: a longitudinal study and an intervention[END_REF]. This process has a lot in common with 'self-efficacy' that Hattie (2018) is using in his work. Hattie emphasizes the strong correlation between self-efficacy (the confidence that students have in themselves and that can make their learning happen) and student achievement.

Mathematics is eminently a subject where mindset plays an important role. On the one hand, the discipline is highly regarded in our society and it is often associated with something you are good at or not. Good grades for mathematics are seen as a clear proof for being intelligent. And parents compare the results of their children quickly with their own school experience and, unconsciously, emphasize the perspective of being either good or bad in it. Unluckily all these aspects foster a fixed mindset. On the other hand, doing mathematics can give students frustration when they do not see the solution right away. Consequently, working with a growth mindset will help them a lot.

Many ideas for mathematical activities that invite students to develop a growth mindset are provided by Boaler [START_REF] Boaler | Mathematical mindset[END_REF]. Some of these interventions, especially the ones that are also described in the studies of Yeager & Welton (2011), [START_REF] Blackwell | Implicit theories of intelligence predict achievement across an adolescent transition: a longitudinal study and an intervention[END_REF], and [START_REF] Hattie | Visible learning, A Synthesis of Over 800 Meta-Analyses Relating to Achievement[END_REF], have been tested in the school year 2016-2017 at the Goois Lyceum, a secondary school in a small town in the Netherlands.

The evaluation of these tests showed that three main elements of the intervention were easy to implement and were experienced as very valuable: (1) an introduction to the theory of mindset and the importance of neuroplasticity, (2) attention for the importance of learning from errors in the teaching process, and (3) classroom as well as individual growth mindset feedback.

In this study, we investigated to what extent this growth mindset-oriented intervention can improve students' attitude towards mathematics.

Method

During the school year 2017-2018 the intervention was further developed and implemented in the first grade of secondary school (grade 7) and in upper secondary school mathematics A classes (mainly grade 10). Grade 7 was chosen because these students recently switched to a new school. In upper secondary education, classes with mathematics A were chosen because mathematics A (preparing for humanities) is seen as 'easier' than mathematics B (preparing for natural sciences). These students often feel that they have chosen a 'lower' form of mathematics and that they cannot perform well in this subject. This lower self-efficacy might indicate a fixed mindset, and it is interesting to see whether this can be changed by the interventions. We advertised the possibility to join the project in a newsletter reaching mathematics teachers all over the Netherlands. In total 512 students in 21 classrooms, from nine schools, joined the experiment, of which 383 filled in both the questionnaires.

Preparation of the teachers

The teachers that were involved in the intervention were given a training of 5 hours at Utrecht University in which the theory of mindset was explained. During the training, teachers got the opportunity to work on some sample activities (low-floor-high-ceiling tasks, Boaler, 2016, or 'My favorite no', [START_REF] Alcala | My favorite no[END_REF] followed by an extensive instruction of the different elements of the intervention. The presentations of the training, the presentations and tasks for the students, and suggestions for further reading were shared online. During the intervention there was a regular exchange of experiences, questions and information through email with the teachers. The intervention contained the following three main elements:

1) Explanation about mindset and the functioning of the brain (neuroplasticity). Although the theory of mindset is a psychological theory it is well supported by brain researchers in relation to the plasticity of the brain (e.g. Woollett & Maguire, 2011;[START_REF] Helden | De lerende mens; over dat we ons leven lang kunnen leren![END_REF]. Nerve cells, or neurons, can make better and more connections throughout our lives (or loose connections when not in use). This allows a rich distributed dynamic network with many opportunities to learn new things, also referred to as neuroplasticity. Because of this neuroplasticity people have the opportunity to learn and expand their knowledge. It is not just the capacity to learn a new language but also new hobbies and new habits. For example, if you fear failure through training you can learn to become more confident [START_REF] Hanson | Buddha's brain; The Practional Neuroscience of Happiness, Love and Wisdom[END_REF]. It is like walking a new path through the jungle; first you need a machete to break through, but after some time when you use the same track more often, a path is created and it gets easier and easier to travel.

At the schools this part of the intervention started with a presentation for all students on the functioning of the brain and on the theory of mindsets. The corresponding task was to make a difficult mathematical assignment without the explanation of new theory. A student with a fixed mindset would not like this, they avoid starting out of fear of making mistakes. A student with a growth mindset would like to continue, thinking "I'm going to try it" or "If it doesn't work out I ask it." The role of the teacher is to give the right growth feedback and to regularly remind students of the neuroplasticity of the brain.

2) The importance of making mistakes and learning from errors. Brains of people who make mistakes with a growth mindset are more active than the brains of someone who makes mistakes with a fixed mindset [START_REF] Boaler | Mathematical mindset[END_REF]. When students do not understand the assignment right away and they are thinking with a fixed mindset, they might believe "Now everyone will notice that I am not smart." They start to get stressed and stress hormones ensure that no new connections between the neurons grow (Dirksen, 2012). Students with a growth mindset will see obstacles more as challenges. They can see that making a mistake is the beginning of learning something new [START_REF] Chödrön | The places that scare youa guide to fearlessness[END_REF]. They then start to feel more confident which in turn sets the brain in a responsive mode, and this stimulates making new connections in the brain [START_REF] Hanson | Buddha's brain; The Practional Neuroscience of Happiness, Love and Wisdom[END_REF]. The teachers are stimulated to use feedback like "I want to understand the way you think and together we can discover what the next step is."

This intervention started with a presentation about the function of making mistakes and the role of mindset. The teachers started several lessons with "My favorite no" [START_REF] Alcala | My favorite no[END_REF]. To change the way in which teachers cope with mistakes is also an aspect of this intervention.

3) The use of feedback. It is important that teachers are aware of the feedback they give, especially while making errors. If they say "what a stupid mistake" they can bring students more towards a fixed mindset. And it is not just the words but also the body language and tones they use. The challenge is to give feedback not on properties or features but on the process [START_REF] Boaler | Mathematical mindset[END_REF]. It may seem great to hear that you are smart. However, it is a kind of label, leading to overconfidence, or to self-doubt like: yes I am smart now but what if I make a mistake, will they call me dull-brained? [START_REF] Mueller | Praise for intelligence can undermine children's motivation and performance[END_REF]. When giving feedback on the process it should be true feedback; only when a student has really worked hard one can evaluate this.

It is not just the feedback that students get from others, it is also the feedback they give themselves.

In a class, it is helpful to listen carefully to what students say while making the assignments or as they chat. For example, when they say "this is too hard", this can be associated with a fixed mindset. Whereas when they are saying "this may take some time" this can be associated with a growth mindset.

The attitude of the teacher is important; when a teacher, from a fixed mindset, has the opinion that the performance of the students stays the same throughout the year it might lead to stagnation. On the other hand, when a teacher, from a growth mindset, believes that the performance of the students can grow than students evolve more easily. Good teachers believe in development of intelligence and talent, which is a growth mindset, and they are fascinated by the learning process [START_REF] Dweck | Mindset, The new psychology of success[END_REF].

At the start of this intervention on feedback the students were shown a short presentation on feedback, words, and the link to mindset. The assignments they then got were low-floor-high-ceiling tasks, for example "what is the largest surface you can make with 36 piles of 1 meter?". Students can easily start and while working can make things more and more difficult. The teacher helps them by giving growth and encouraging feedback and challenge them.

To participate in this study teachers were askedas a minimal requirementto teach the previously described elements of the intervention (on the plasticity of the brain and the consequences for learning, the importance of errors, and the role of feedback in learning). Furthermore, they were asked to implement at least one growth-mindset task with every intervention. Finally, they were invited to examine their own attitude towards mistakes and to practice with growth-mindset feedback in their classroom.

Procedure of the intervention

At the start and at the end of the intervention, students filled in a questionnaire to determine their mindset. This questionnaire consisted of 25 statements that were compiled from the literature of Blackwell and Dweck [START_REF] Blackwell | Implicit theories of intelligence predict achievement across an adolescent transition: a longitudinal study and an intervention[END_REF][START_REF] Dweck | Mindset, The new psychology of success[END_REF]. Students were asked to label their level of agreement to the statements on a 6-point Likert scale. During the interventions at five schools a lesson with the intervention was observed and students and teachers were interviewed about their experiences.

Results

In Figure 1 the mean differences in the total score of the questionnaire are represented. It can be seen that in only five classes the total scores after the interventions had lowered, indicating a more fixed mindset. In the remaining sixteen classes the scores went up, indicating a more growth mindset. The Grade 7 classes are drawn in black and Grade 10 in blue, with no clear differences emerging.

Figure 1. The mean differences in the total scores per class

In Table 1 the average scores on the different scales are given for the two grades. It can be seen that the effect of the interventions is most clear for the mindset score (e.g. +3.1 for the Mindset scale in Grade 7). Both in Grade 7 and Grade 10 the post intervention mindset scores are higher. In Table 2 the results of the changes of the individual students show a similar pattern of more pronounced changes in the mindset score compared to the scores in the other domains. Also, here the change towards a more growth mindset is larger in the Grade 7 classes (67.5%). This trend may indicate that the mindsets of the Grade 7 students are more intensely influenced by the interventions. All the teachers were very much involved in the intervention. During the interviews they made comments like: "As a mentor, and as a teacher in mathematics, I can now discuss more easily how important it is to learn from your mistakes. I also designate my own mistakes more consciously, and I explain how I deal with them.''

Another teacher writes that she has become more careful with her words. Even small, seemingly unimportant words like quickly (make your assignments quickly) she tries to avoid as it disempowers her lessons. The classes that show a decrease or stability in mindset scores are one Grade 7 class and two Grade 10 classes. Two of these teachers were starting teachers who were very enthusiastic about the intervention but for whom teaching itself was relatively new. The third teacher was a more experienced teacher and also very committed to the interventions. However, in his class there were a lot of changes in the composition of the class, which may have influenced the outcome.

The questionnaire at the end of the intervention included questions about which part of the intervention the students appreciated most. They valued the entire intervention because of its content and also because of the changes in their teacher's attitudes. The lesson on the brains and on the mistakes were most highly appreciated. One student explained: "I have to stop thinking 'this will cost too much time', or 'I really cannot do this'; instead I can persevere or try again later."

The personal interviews with students also revealed that the lesson on making mistakes was experienced as the most positive, though also after the interventions one student made the following remark: "I did learn that making mistakes does not matter, however I still do not like it."

Students and teachers reported during the interviews that an important element of working with mindset is the use of words. One student noticed "It sometimes seems as if we have learned a new language together." Another student said "Sir, this feels like a fixed remark, do you mean it like that?" One teacher said: "I find it a real challenge, you have to pay attention to all the words the students are saying, also the words they say to each other and to themselves. To be able to do that of all the students is not (yet) possible, however with a few students separately I do succeed."

Discussion

The mindset theory addresses issues that are highly relevant for current teaching practices in mathematics education. We are aware that changing teachers' teaching and students' learning behavior can hardly be achieved through a one-day training for teachers. Nevertheless, this study shows that teachers did become sensitive for changing their practice towards fostering a growth mindset after a training of only five hours and some initial experiences with the interventions. From this study, the effects of changing practices on student achievements are not clear. What it does show is an obvious attitude change towards students' own learning and towards the importance of making mistakes in learning mathematics. These are important first steps towards a changing culture in the mathematics classrooms. Finally, teachers reported that the mindset theory provides an inspirational vocabulary and set of tools to implement and improve daily teaching practices.

The training of teachers was first seen as a preparation for the three elements of the intervention mentioned above, but actually it turned out to be a separate intervention. Once teachers were familiar with the theory of the mindset they changed their lessons: teachers were more aware of the mindset from which they taught their students, of the importance of learning from their mistakes and the feedback they gave. And this had a direct impact on the mindset of their students.

  The statements were divided in four types: mindset, effort belief, response to failure, and learning goals. With these different types the impact of the intervention could be measured in different domains. Example questions were:

Q1. You have a certain amount of intelligence and you cannot do much to change it Q3. An important reason why I do my schoolwork is because I like to learn new things Q5. It does not matter who you are and where you come from, you can always change your level of intelligence Q16. If you have to work hard for a subject, you are probably not very good at it.

Table 1 : Results of the scores of the pre-and posttest (the questionnaire before and after the mindset interventions); the average of the different grades in the different domains

 1

	(Grade 7 N = 246 Grade 10 N = 137)
	Sub scale	Grade level	Pretest		Posttest		Difference
			M	SD	M	SD
	Mindset	Grade 7	27.8	6.8	30.9	6.6	+3.1
		Grade 10	27.1	6.2	29.0	7.0	+1.9
		Total	27.5	6.5	30.2	6.8	+2.6
	Learning goals	Grade 7	16.2	3.4	15.6	3.8	-0.6
		Grade 10	14.3	3.6	14.8	3.7	-0.5
		Total	15.5	3.6	15.3	3.8	-0.2
	Effort belief	Grade 7	28.8	3.4	29.0	3.7	+0.2
		Grade 10	27.3	3.3	27.8	3.8	+0.5
		Total	28.2	3.5	28.5	3.8	+0.3
	Response to failure Grade 7	38.8	4.9	38.8	5.0	0.0
		Grade 10	37.5	5.4	36.9	5.8	-0.6
		Total	38.4	5.1	38.1	5.3	-0.3
	Total score	Grade 7	111.6	12.9	114.2	12.8	+2.6
		Grade 10	106.3	13.2	108.4	14.8	+2.1
		Total	109.7	13.2	112.1	13.8	+2.5

Table 2 : Results of the changes of the individual students Change on Percentage of changes * Difference between grade 7 and 10

 2

	Total score	39.7% negative change	Grade 7: 38.6% negative, 6.1% =, 55.4% positive
		4.7% no change	Grade 10: 41.6% negative, 2.2% =, 56.2% positive
		55.6% positive change
	Mindset score	29.0% negative	Grade 7: 26.4% negative, 6.1% =, 67.5% positive
		7.3% no change	Grade 10: 33.6% negative, 9.5% =, 56.9% positive
		63.7% positive
	Learning goals	45.2% negative	Grade 7: 49.6% negative, 16.3% =, 34.1% positive
		14.4% no change	Grade 10: 37.2% negative, 10.9% =, 51.8% positive
		40.4% positive
	Believe in effort	39.7% negative	Grade 7: 42.7% negative, 12.2% =, 45.1% positive
		14.6% no change	Grade 10: 34.3% negative, 19.0% =, 46.7% positive
		45.7% positive
	Response to failure	45.4% negative	Grade 7: 41.9% negative, 15.9% =, 42.3% positive
		14.1% no change	Grade 10: 51.8% negative, 10.9% =, 37.2% positive
		40.5% positive

* a negative change is a change towards a fixed mindset; a positive change is a change towards a growth mindset.

Acknowledgments

We would like to acknowledge all the students and teachers that have worked with the interventions. We have learned so much from all of you. Thanks for being so open to all new ideas. Also thanks to everyone from The Goois Lyceum, for being experimental subject in this study.


Alexei Sharonov

Thomas Gustavsson

Sylvie Marguet

Dimitra Markovitsi
email: dmarkovitsi@cea.fr

Photophysical properties of 5-methylcytidine

Cytosine methylation, which determines the hot spots for DNA photo-damage, is shown to induce a red-shift of the nucleoside absorption spectrum, making the chromophore more vulnerable to solar radiation, and a tenfold increase of the fluorescence lifetime, making excited state reactions more probable. A femtosecond investigation of the excited state deactivation reveals a quite complex mechanism.

Introduction

DNA methylation and demethylation, occurring on position 5 of cytosine bases, are natural processes which play a key role in biological functions such as regulation of gene expression and genome reprogramming. 1,2 Moreover, cytosine methylation determines the hotspots of DNA damage [START_REF] Denissenko | Cytosine methylation determines hot spots of DNA damage in the human P53 gene[END_REF] which can be induced by sunlight. [START_REF] You | Similarities in sunlight-induced mutational spectra of CpG-methylated transgenes and the P53 gene in skin cancer point to an important role of 5-methycytosine residues in solar UV mutagenesis[END_REF] Despite the fact that 5-methylcytosine is a preferential target for carcinogenic mutation caused by UV radiation, the underlying photophysical and photochemical mechanisms are not understood. A few publications report the characterisation of the reaction products obtained upon exposure to the UV light of aqueous solutions in which 5-methylcytosine was present as a nucleobase [START_REF] Privat | Photochemical deamination and demethylation of 5-methylcytosine[END_REF] or incorporated in dinucleosides and polynucleotides. 6-8 But, so far, the properties of the excited states and in particular their relaxation dynamics remain unknown. Regarding the first singlet excited state, the lack of such information is due to its very short lifetime. Only very recently has it been possible to study the excited state dynamics of the four common DNA bases, nucleosides and nucleotides by absorption 9,10 and fluorescence 11-14 spectroscopy with femtosecond resolution.

As a continuation of our work on the photophysical properties of DNA components, [START_REF] Gustavsson | Thymine, thymidine and thymidine 5Ј-monophosphate studied by femtosecond fluorescence upconversion spectroscopy[END_REF][START_REF] Gustavsson | Adenine, deoxyadenine and deoxyadenine 5Ј-monophosphate studied by femtosecond fluorescence upconversion pectroscopy[END_REF][START_REF] Onidas | Fluorescence properties of DNA nucleosides and nucleotides: a refined steady-state and femtosecond investigation[END_REF][START_REF] Bouvier | Dipolar coupling between electronic transitions of the DNA bases and its relevance for exciton states in double helices[END_REF][START_REF] Markovitsi | Effect of molecular organisation of DNA oligomers studied by femtosecond fluorescence spectroscopy[END_REF] we have undertaken a study of 5-methyl-2Ј-deoxycytidine (5m-dC) (Fig. 1) using steadystate absorption and fluorescence spectroscopy as well as time-resolved fluorescence spectroscopy with femtosecond resolution based on the upconversion technique. We report here its behaviour in comparison with that of the non-methylated analogue (dC) studied previously. 14 Experimental 5-Methylcytidine was purchased from Sigma Aldrich and used without further purification. It was dissolved in ultrapure water produced by a MILLIPORE (Milli-Q Synthesis) purification system.

Steady-state absorption and fluorescence spectra were recorded using a Perkin Lambda 900 spectrophotometer and a SPEX Fluorolog-2 spectrofluorometer, respectively. Fluorescence quantum yields ( ) were determined for 10 Ϫ5 M solutions using quinine sulfate dihydrate in 0.1 M HClO 4 ( = 0.59). [START_REF] Velapoldi | A Fluorescence Standard Reference Material: Quinine Sulfate Dihydrate[END_REF] Time-resolved fluorescence measurements were performed by the upconversion set-up described in detail elsewhere. 12, [START_REF] Gustavsson | Adenine, deoxyadenine and deoxyadenine 5Ј-monophosphate studied by femtosecond fluorescence upconversion pectroscopy[END_REF] The third harmonic of a mode-locked Ti:sapphire laser (267 nm) was used for excitation and the spectral resolution at the detection wavelength was set to 8 nm. Parallel (I par ) and perpendicular (I perp ) excitation/detection configurations were realized by controlling the polarization of the exciting beam with a half-wave plate. The fluorescence decays presented here were calculated as I par ϩ 2I perp . The apparatus function was 420 fs (fwhm). Temporal scans were made in a 30 ps timewindow with 100 fs steps. The zero time was defined at the half maximum of the signal rise. Spectra were recorded directly by simultaneously changing the monochromator wavelengths, rotating the upconversion crystal, and changing the delay line position in order to compensate for group velocity dispersion. [START_REF] Gustavsson | Femtosecond spectroscopic study of relaxation processes of three aminosubstituted coumarin dyes in methanol and dimethyl sulfoxide[END_REF] Subsequently, they were corrected for the spectral response of the detection system.

Solutions (2 × 10 Ϫ3 M) were kept flowing in a 0.4 mm quartz cell, which also was kept in continuous motion perpendicular to the excitation beam. Successive recordings with the same solution gave reproducible signals, showing that photodegradation does not affect the measurements.

All measurements were performed at room temperature (20 ± 1 ЊC) under aerated conditions.

Results

The absorption spectrum of 5m-dC in aqueous solution peaks at 278 nm (Fig. 2). It is somewhat less intense and shifted to longer wavelengths in comparison with the spectrum of dC. The shift, determined at the absorption maximum, is 1000 cm Ϫ1 .

The fluorescence spectra recorded for 5m-dC upon excitation at wavelengths ranging from 250 to 300 nm are all identical and peak at 342 nm (Fig. 3). They are also red-shifted with respect to the dC spectra (by 1200 cm Ϫ1 at the emission maxima). Neither the absorption nor the fluorescence spectra show any concentration dependence in the range 10 Ϫ5 Ϫ 2 × 10 Ϫ3 M, except reabsorption of the emitted photons below 305 nm.

The fluorescence quantum yield of 5m-dC was found to be (5.6 ± 0.1) × 10 Ϫ4 . This value is about six times higher than that determined by us for dC (0.89 × 10 Ϫ4 ). [START_REF] Onidas | Fluorescence properties of DNA nucleosides and nucleotides: a refined steady-state and femtosecond investigation[END_REF] All the fluorescence decays recorded for 5m-dC aqueous solutions at various wavelengths upon excitation at 267 nm are much slower than the dC ones. For example, it can be seen in Fig. 4 that 99% of the signal recorded for dC at 330 nm has disappeared at 5 ps, whereas for 5m-dC this happens only at 25 ps. In contrast to dC, a clear wavelength dependence can be observed for 5m-dC. Upon increasing the wavelength from 310 nm to 350 nm, the decays become drastically slower and slower (Fig. 5). Above 350 nm, the behaviour is still present although much less pronounced. The apparent rise of the signal observed in Fig. 5 is identical for all wavelengths and is due only to the instrumental response function.

The decays were fitted with bi-exponential functions α exp(Ϫt/τ 1 ) ϩ (1 Ϫ α)exp(Ϫt/τ 2 ) from which average decay times 〈τ〉 = ατ 1 ϩ (1 Ϫ α)τ 2 were determined. The results of the fits are shown in Table 1. The τ 1 values vary from 0.6 to 1.3 ps and the τ 2 values from 4.3 to 6.1 ps. The average decay time is only 1.2 ps at 310 nm and reaches a rather constant value of 3.9 ± 0.3 ps at longer wavelengths. This is more than one order of magnitude higher than the average decay time found for dC (0.3 ps). [START_REF] Onidas | Fluorescence properties of DNA nucleosides and nucleotides: a refined steady-state and femtosecond investigation[END_REF] It should be noticed that the relatively high uncertainties found for the values at 420 nm are due to the weak signal intensity at this wavelength.

The integrated fluorescence spectrum of 5m-dC recorded with the upconversion set-up compares quite well with the corresponding steady-state spectrum (Fig. 3). This means that the fluorescence decays do not contain any important long lived component having a different spectrum than that detected with the upconversion technique. During the first few picoseconds the time-resolved fluorescence spectra decrease in intensity, shift to the red and become narrower. This is illustrated in Fig. 6 where the spectra recorded at 200 fs, corresponding to the emission maximum, and at 5 ps are shown together. The spectrum at 5 ps is shifted to lower energies by 400 cm Ϫ1 and its width (fwhm) is reduced by 1300 cm Ϫ1 , compared to the spectrum at 200 fs. 0.36 ± 0.04 0.9 ± 1.1 5.8 ± 0.9 4.0

Discussion

A red-shift of the absorption and fluorescence spectra, as well as an increase in the fluorescence quantum yield and the fluorescence lifetime found for 5m-dC as compared with dC, has also been observed upon methylation of other DNA components. For example, the fluorescence quantum yield of 7-methylguanosine is two orders of magnitude higher than that of guanosine. 14, [START_REF] Georghiou | Excited-state properties of DNA methylated at the N-7 position of guanine and its free fluorophore at room temperature[END_REF] The important point here is that 5m-dC, which is naturally present in the human genome, can absorb more photons than the four common DNA nucleosides in the UVB region of the solar spectrum and the longer lifetime of its first excited state increases the probability for the photoreactions to occur.

Regarding singlet excited state relaxation, we have reported previously that the fluorescence decays of all DNA nucleosides in aqueous solution cannot be described by single exponentials. [START_REF] Onidas | Fluorescence properties of DNA nucleosides and nucleotides: a refined steady-state and femtosecond investigation[END_REF] However, in contrast to 5m-dC, no clear wavelength dependence in the fluorescence decays could be detected for adenosine, cytidine, guanosine and thymidine. It should be kept in mind that the very short lifetimes, compared to the apparatus function, of these compounds makes it difficult to characterise the spectral dynamics.

The specific behaviour of 5m-dC may have various origins. The simplest one is that the ground state is a mixture of tautomers with different fluorescence spectra and fluorescence lifetimes. However, this hypothesis can easily be ruled out because the shape of the steady state fluorescence spectrum does not depend on the excitation wavelength. Thus, the observed inhomogeneity is likely to arise from the multiple processes involved in excited state relaxation. Emission from hot vibrational levels could be responsible for the relatively faster decay at the blue side of the fluorescence spectrum. Such a process should result in a spectral narrowing as a function of time which is in agreement with the experimental data (Fig. 6). Another effect which may interfere is solvent rearrangement causing a red shift of the fluorescence spectrum, which is also observed for 5m-dC (Fig. 6). A recent investigation carried out for aqueous solutions of 2-aminopurine, a modified DNA base, showed that solvation takes place at the time-scale probed in our experiments. [START_REF] Pal | Ultrafast decay and hydration of DNA bases and mimics[END_REF] Finally, we cannot exclude complex deactivation mechanisms involving several electronic states or proton/hydrogen exchange between the chromophore and surrounding water molecules. A study of the fluorescence dynamics of 5m-dC as a function of the solvent should help to elucidate the various factors playing a role in excited state relaxation.

Fig. 1

 1 Fig. 1 DNA nucleosides.

Fig. 2

 2 Fig. 2 Absorption spectra of 5m-dC (solid line) and dC (dashed line) in aqueous solution.

Fig. 3

 3 Fig. 3 Fluorescence spectra of of 5m-dC (solid line) and dC (dashed line) in aqueous solution; λ ex = 255 nm. The circles correspond to the total fluorescence recorded by the upconversion technique.

Fig. 4

 4 Fig.4 Fluorescence decays recorded at 330 nm for 5m-dC (filled circles) and dC (squares) fitted by bi-exponential functions.

Fig. 5

 5 Fig.5 Fluorescence decays recorded for 5m-dC aqueous solutions at 310 nm (squares), 330 nm (triangles) and 370 nm (circles) upon excitation at 267 nm.

Fig. 6

 6 Fig. 6 Time-resolved fluorescence spectra recorded for 5m-dC aqueous solutions at 200 fs (circles) and 5 ps (squares).

Table 1

 1 Characteristic times/ps of the 5-methyl-2Ј-deoxycytidine fluorescence decays resulting from fitting to bi-exponential functions α exp(Ϫt/τ 1 ) ϩ (1 Ϫ α)exp(Ϫt/τ 2 )

	λ/nm	α	τ 1 /ps	τ 2 /ps	〈τ〉/ps a
	310	0.82 ± 0.01	0.56 ± 0.08	4.3 ± 0.4	1.2
	330	0.6 ± 0.01	1.0 ± 0.1	5.4 ± 0.3	2.8
	350	0.46 ± 0.01	1.1 ± 0.2	5.7 ± 0.3	3.6
	370	0.38 ± 0.01	0.9 ± 0.1	5.7 ± 0.1	3.9
	380	0.39 ± 0.01	1.3 ± 0.2	6.1 ± 0.3	4.2
	420

a 〈τ〉 = ατ 1 ϩ (1 Ϫ α)τ 2 .

Acknowledgements

Financial support from the CEA programme "Toxicologie Nucléaire" is gratefully acknowledged. The authors thank Dr J. Bernardino for stimulating discussions.

Notes and references


Quentin Jamet
email: qjamet@fsu.edu

W K Dewar

N Wienders

B Deremble

Fast warming of the surface ocean under a climatological scenario

Weakly varying climatological winds reduce upper ocean vertical mixing, affecting the redistribution of air-sea fluxes • Coupled to an atmospheric boundary layer, the modeled ocean response to climatological winds is to warm up considerably at the surface • Results illustrate the pivotal improvements in air-sea interactions achieved by driving an ocean model with an atmospheric boundary layer

Introduction

The ocean is one of the most important components of the climate system due to its large heat capacity. Understanding its dynamics remains challenging due to interactions with the other components of the climate system, particularly the atmosphere. It is common to decouple the climate system to reduce its complexity: A well known strategy is to use ocean-only numerical simulations for which air-sea interactions are control variables that one can adjust to study the ocean responses. However this approach strongly relies on parameterizations used to represent these interactions. We study here oceanonly models driven by different surface forcing strategies with the view toward assessing strengths and weaknesses of each.

Modeling a variable ocean under a specified but variable atmosphere is a useful and efficient idealization. However, some studies have highlighted an important caveat of this approach. [START_REF] Huck | Linear stability analysis of three-dimensional thermally-driven ocean circulation: application to interdecadal oscillations[END_REF] have found that large scale modes of variability (Colin de Verdière and Huck, 1999;[START_REF] Huck | Interdecadal variability -13-manuscript submitted to Geophysical Research Letters of the thermohaline circulation in box-ocean models forced by fixed surface fluxes[END_REF] only appear if the ocean model was forced by prescribed fluxes rather than a prescribed atmosphere. In the first case (prescribed air-sea fluxes), the ocean is not as constrained as in the second case where the atmospheric conditions maintain the ocean in a state close to the forcing conditions. Additionally, [START_REF] Rahmstorf | The role of temperature feedback in stabilizing the thermohaline circulation[END_REF] have shown that large scale ocean feedbacks on the -2-manuscript submitted to Geophysical Research Letters atmospheric temperature have significant impacts on the rate of the overturning circulation in the North Atlantic. Such feedbacks are not considered when the ocean surface is restored toward prescribed atmospheric conditions. These results illustrate the limitations associated with a prescribed atmospheric forcing, where the assumption of an infinite heat capacity for the atmosphere interferes with the development of internal ocean dynamics.

Following these ideas, we wish to assess if similar limitations would be at work for the development of an oceanic state of equilibrium under climatological winds. This question arises from the recognized contribution of the fast varying winds associated with synoptic weather systems to maintain realistic turbulent air-sea fluxes [START_REF] Gulev | Influence of space-time averaging on the ocean-atmosphere exchange estimates in the north atlantic midlatitudes[END_REF][START_REF] Hughes | Averagingrelated biases in monthly latent heat fluxes[END_REF][START_REF] Jung | The oceanic response to mesoscale atmospheric forcing[END_REF][START_REF] Ponte | Nonlinear effects of variable winds on ocean stress climatologies[END_REF][START_REF] Wu | Impact of synoptic atmospheric forcing on the mean ocean circulation[END_REF][START_REF] Zhai | On the wind power input to the ocean general circulation[END_REF] and upper ocean vertical mixing [START_REF] Condron | The impact of polar mesoscale storms on northeast Atlantic Ocean circulation[END_REF][START_REF] Holdsworth | The influence of high-frequency atmospheric forcing on the circulation and deep convection of the Labrador Sea[END_REF][START_REF] Wu | Impact of synoptic atmospheric forcing on the mean ocean circulation[END_REF]. This high frequency atmospheric variability is indeed filtered out by the averaging used to construct climatological products, such that the high frequency wind variance strongly reduces at mid-and high latitudes (Fig. 1, top panels). Forcing an ocean model with climatological winds is therefore expected to significantly modify air-sea fluxes and upper ocean vertical mixing. It is however less clear how the ocean will adjust to such a forcing if thermodynamic ocean feedbacks on the atmosphere are considered.

To identify the oceanic state that develops under climatological winds, we propose to work with an atmospheric boundary layer (CheapAML; [START_REF] Deremble | Cheapaml: A simple, atmospheric boundary layer model for use in ocean-only model calculations[END_REF]. With this strategy, the assumption of an infinite atmospheric heat capacity is relaxed and atmospheric temperature and humidity can respond to ocean surface structures. A detailed description of the model strategy is given in Section 2. The ocean response to climatological winds in this framework is described in Section 3. We compare these results with those obtained with a more traditional representation of air-sea fluxes, i.e. when the atmosphere is prescribed, in Section 4, and assess the relevance of a 'normal' year to maintain high frequency winds in Section 5. Finally, we conclude and discuss the results in Section 6.

-3-manuscript submitted to Geophysical Research Letters

Numerical Experiments

We use the MIT general circulation model (MITgcm; [START_REF] Marshall | A finitevolume, incompressible Navier Stokes model for studies of the ocean on parallel computers[END_REF]) in a regional configuration of the North Atlantic: the domain extends from 20 • S to 55 • N with a horizontal resolution of 1 4

• (see Supporting Information). The mixed layer depth computed by the non-local K-Profile Parametrization (KPP) scheme of [START_REF] Large | Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization[END_REF] is used in the heat budget of Section 3.2.

At the surface, different strategies are used to force the ocean model and look at their impact on the ocean dynamics. In a first set of experiments, we couple the ocean model to the atmospheric boundary layer model CheapAML [START_REF] Deremble | Cheapaml: A simple, atmospheric boundary layer model for use in ocean-only model calculations[END_REF]. With this approach, we better represent the air-sea exchanges, and we also let the ocean develop its internal dynamics (not necessarily correlated to a prescribed atmospheric state).

In CheapAML, winds are assumed to be the least sensitive atmospheric variable to ocean surface structure, and are thus prescribed. The remaining atmospheric variables, i.e. temperature and humidity, are advected by these prescribed winds and are modified by the air-sea fluxes. Over the ocean, the temporal evolution of these atmospheric variables is computed using a forced advection-diffusion equation. Over land, temperature and humidity are strongly relaxed toward the reanalysis prescribed values. The atmospheric variables prescribed in CheapAML are applied every 6 hours and derived from the Drakkar forcing set (cf Supporting Information). This configuration is run for 10 years in three different experiments. In the first one, referred to as AML FULL, we use the full range of atmospheric time scales, from sub-daily (6-hourly) to interannual, over the period 1958-1967. In the second one, referred to as AML CLIM, we use a yearly repeated climatological atmospheric seasonal cycle. To consistently filter the year-to-year atmospheric variability, the climatology has been computed as an ensemble average of all the years between 1958-1977. This second experiment is run for 10 years, i.e. for the same duration as the first experiment. In the third experiment, referred to as AML NY, we use a yearly repeated 'normal' year forcing [START_REF] Large | Diurnal to decadal global forcing for ocean and sea-ice models: the data sets and flux climatologies[END_REF], constructed as the realistic atmospheric forcing from Au- To understand how the atmospheric temperature and humidity in CheapAML responds to the ocean surface dynamics, two additional experiments are conducted where all atmospheric variables (wind, atmospheric surface air temperature and humidity) are prescribed. This strategy is commonly used in the ocean modeling community and it will serve as a reference test case to which we will compare our experiments. With these prescribed atmospheric variables, we compute the air-sea fluxes the same way as the previous cases but there is no feedback on the atmospheric temperature and humidity. As in AML FULL and AML CLIM we run two experiments with either fully varying or climatological winds. We name these two experiments FORC FULL and FORC CLIM, respectively.

Fully Varying vs Climatological Wind Experiments

Because the Sea Surface Temperature (SST) is an oceanic variable sensitive to airsea exchange, we first compare the model SST for the two experiments AML CLIM and AML FULL (Fig. 2, top panels) after 10 years of simulation. The yearly averaged SST differences between the two experiments are very large in amplitude, reaching more than 8 • C in the subtropical gyre, and spreading over the North Atlantic, north of 20 • N. At the center of the subtropical gyre where the largest SST differences are observed, the time evolution of SST over the course of the 10 years of simulation reveals that such large differences are reached quickly, after 5 months, suggesting a fast dynamic response of the ocean. The mechanism that drives the warming of the subtropical gyre in the AML CLIM experiment is described in the two following sections. We focus on the first two years of simulation where most of the differences build up.

Heat Fluxes

In our configuration, the components of the net heat fluxes which vary from experiment to experiment are the latent and sensible fluxes, as well as the outgoing longwave radiation associated with the SST (the other components are prescribed). We discuss their respective contribution for the net heat fluxes in the following.

In AML FULL, the time mean and standard deviation of the latent and sensible heat fluxes (computed over the 10 years of simulation) are 117±37 and 8±8 W m -2 , respectively. Added together, these fluxes are sufficiently strong to induce positive (up--5-manuscript submitted to Geophysical Research Letters ward) net heat fluxes during the first two months of simulation (Fig. 3, top panel). They contribute to the cooling of the ocean surface at the beginning of the simulation which is consistent with winter time (January-February). In AML CLIM, the turbulent fluxes are reduced by more than 50% (57±19 W m -2 ; 1±1.4 W m -2 for latent and sensible heat fluxes, respectively), consistent with earlier results [START_REF] Hughes | Averagingrelated biases in monthly latent heat fluxes[END_REF]. As a consequence, the too weak turbulent heat fluxes lead to negative (downward) net heat fluxes, contributing to the warming of the surface ocean at the beginning of the simulation (top right panel of Fig. 2).

The mechanisms that drive the reduction in turbulent air-sea fluxes are further investigated by looking at the sensible heat flux amplitude In AML CLIM, the air-sea temperature differences do not exceed ±1 • C (Fig. 3, bottom right panel), while they range from about -2 • C to about +4 • C in AML FULL. Under fully varying winds, there are thus oceanic processes that take the ocean surface away from the overlying atmosphere and lead to larger air-sea temperature differences. We show in Section 3.2 that those processes are associated with upper ocean vertical mixing.

S = ρ A C (A) p |u|(SST -T a - γh), with ρ A = 1.3 kg m -3 , C (A) p = 1004 J kg -1 K -1 , γ = 0.0098 K m -
As the ocean surface quickly warms up at the beginning of the simulation when exposed to climatological winds, the outgoing longwave radiation increases accordingly (outgoing longwave radiation is proportional to SST 4 ). The system reaches a new state af- Note that since atmospheric downward longwave radiations are prescribed, the radiative effects of a warmer atmosphere are not considered. Such an effect would positively contribute to the upper ocean warming since increased downward longwave atmospheric radiations would induce larger warming of the ocean surface (Fig. S3).

Oceanic Vertical Mixing

We now describe the differences between the two equilibria in terms of oceanic dynamics. We performed a heat budget following [START_REF] Peter | A model study of the seasonal mixed layer heat budget in the equatorial atlantic[END_REF] for the box at the center of the subtropical gyre where the SST difference is the largest. The temperature tendency ∂ t T within the mixed layer h(x, y, t) (computed by the KPP parameterization) is decomposed into advective terms, a flux term and dissipation terms (cf Supporting Information). Comparing the results of this heat budget for the two experiments using CheapAML (Fig. S5), the most important difference in the processes controlling the temperature is found to be the upper ocean vertical mixing.

While the upper ocean vertical mixing is relatively constant through the year in AML CLIM with a mixed layer depth which does not exceed 15 m, it exceeds 40 m in AML FULL during winter in response to atmospheric storms. Thus, even though the net heat fluxes in AML CLIM are weaker (cf Section 3.1), their contribution for the heat budget of the mixed layer quickly exceed 0.5 • C/day. In AML FULL by contrast, surface heat fluxes warm a thicker mixed layer, and thus lead to a weaker temperature tendency during the first 5 months of simulation (Fig. S5, top right panel). Also note that, in AML FULL, the vertical diffusion at the bottom of the mixed layer 1 h K z ∂ z T | z=-h controls most of the balance between surface heating and internal ocean processes, i.e. it explains a significant fraction of the residual ∂ t T + Qnet ρ0Cph (Fig. S5, bottom panels).

The other terms (lateral diffusion, advective and entrainment terms; cf Eq. ( 4) in Supporting Information) are at least one order of magnitude smaller. In AML CLIM by contrast, the vertical diffusion at the bottom of the mixed layer is weaker and explains a smaller fraction of that residual. This suggests that the oceanic processes within the mixed layer have changed. We suspect night time convection comes into play, but we cannot draw firm conclusions with the 5-day averaged outputs used in this study.

A Prescribed Atmosphere

Most numerical studies that use climatological atmospheric fields do not use an atmosphere boundary layer model to compute the atmospheric temperature and humidity [START_REF] Grégorio | Intrinsic variability of the atlantic meridional overturning circulation at interannual-to-multidecadal time scales[END_REF][START_REF] Penduff | Sea level expression of intrinsic and forced ocean variabilities at interannual time scales[END_REF][START_REF] Sérazin | Intrinsic variability of sea level from global ocean simulations: Spatiotemporal scales[END_REF]. In order to compare our results with these kind of experiments, we perform two additional runs (FORC FULL and FORC CLIM) for which all atmospheric fields (including temperature and humidity) are prescribed. After 10 years, the simulated SST difference between FORC FULL and FORC CLIM share a relatively similar spatial pattern with the AML experiments (Fig. 2, left panels), but those differences are much weaker, and do not exceed 2.5 • C in the subtropical gyre. Note that, consistent with the temperature difference observed between the two AML experiments, the SST difference observed in the subtropical gyre is also reached after only 5 months of simulation (Fig. 2, right panels).

From these comparisons, we conclude that prescribing the atmospheric state reduces the effects of climatological winds on the temperature of the upper ocean layers.

The underlying physical basis remains however questionable. Due to the weak high frequency variance of the climatological winds, the vertical ocean mixing remains weak. The difference in the mixed layer depth computed by the KPP scheme is very similar to what is shown in Fig. 1 for the AML experiments. As a consequence, the upper ocean tends to warm up in FORC CLIM, but the atmosphere does not. In fact, because the atmospheric temperature is prescribed in this experiment, the ocean-atmosphere temperature differences increase, as shown in Fig. 3 (bottom right panel) for the subtropical gyre. In FORC CLIM, the SST -T a difference is always positive and roughly 2-4 • C. This illustrates the damping role of the atmosphere on the surface ocean temperatures, constraining the upper ocean warming tendency. This increased SST -T a difference counteracts the effect of climatological winds on the turbulent air-sea fluxes, such that for the same wind speed amplitude, the sensible heat fluxes are much larger in FORC CLIM than in AML CLIM and always positive (Fig. 3, top right panel). A similar scenario happens for the latent heat fluxes, which results in turbulent heat fluxes in FORC CLIM which are of comparable amplitude than those found in FORC FULL (Fig. 3, bottom left panel). This is not consistent with previous studies [START_REF] Gulev | Influence of space-time averaging on the ocean-atmosphere exchange estimates in the north atlantic midlatitudes[END_REF][START_REF] Gulev | Climatologically significant effects of space-time averaging in the north atlantic sea-air heat flux fields[END_REF][START_REF] Hughes | Averagingrelated biases in monthly latent heat fluxes[END_REF], where the lack of high frequency wind variance is expected to significantly reduce the magnitude of turbulent air-sea fluxes. In the AML experiments by contrast, since the atmospheric temperature follows the surface ocean warming we have shown that the reduced turbulent heat fluxes under climatological winds are consistently captured and balanced by increased outgoing longwave radiations. Since this latter scenario has better physical consistency, we argue that the dynamically consistent ocean response to an artificial climatological atmosphere is to warm considerably at the surface.

A view toward ocean climate studies

To study the oceanic variability and to distinguish between the atmospherically forced and the internally generated low-frequency oceanic variability, it is common to drive ocean models with climatological winds. When using an atmospheric boundary layer, our results reveal that fast varying atmospheric winds have to be accounted for in order to maintain a realistic oceanic state. Results of the AML NY experiment driven by a 'normal' year forcing [START_REF] Large | Diurnal to decadal global forcing for ocean and sea-ice models: the data sets and flux climatologies[END_REF]) are promising in this respect. Both air-sea turbulent fluxes and the depth of the mixed layer compare well to those diagnosed in AML FULL (not shown). This results in smaller differences in SST between the two experiments (Fig. S2 and S3) compared to those obtained with climatological winds. The oceanic state that develops under a 'normal' year forcing is thus more consistent with the oceanic state that develops under a fully varying forcing. This is likely to make the comparison between For long time scales, where the ocean is expected to control air-sea exchanges [START_REF] Bjerknes | Atlantic air-sea interaction[END_REF][START_REF] Gulev | North Atlantic Ocean control on surface heat flux on multidecadal timescales[END_REF][START_REF] Jungclaus | Low-frequency variability of the arctic climate: the role of oceanic and atmospheric heat transport variations[END_REF][START_REF] Latif | Is the thermohaline circulation changing?[END_REF][START_REF] Shaffrey | Bjerknes compensation and the decadal variability of the energy transports in a coupled climate model[END_REF], there are potential benefits in using an atmospheric boundary layer model to drive ocean-only models. The simulations presented here are however too short to make any statement about low-frequency variability with good accuracy. To illustrate this idea, we have performed an exploratory 50 years, high resolution (1/12 • ) run in a [START_REF] Clement | The atlantic multidecadal oscillation without a role for ocean circulation[END_REF][START_REF] Farneti | Modelling interdecadal climate variability and the role of the ocean[END_REF][START_REF] Zhang | Comment on the atlantic multidecadal oscillation without a role for ocean circulation[END_REF].

-10-manuscript submitted to Geophysical Research Letters

Conclusion

We have revisited the surface forcing strategy used to drive ocean-only models. The analysis of an ocean model in a regional North Atlantic configuration coupled to an atmospheric boundary layer model shows that the oceanic state that develops under climatological winds is much warmer at the surface than the one that develops in a companion experiment driven by fully varying winds. It is up to 8 • C warmer in the North Atlantic subtropical gyre after only 5 months of simulation. Although significantly different than realistic conditions, we argue that those changes are physically consistent, and interpret this new oceanic state as likely when exposed to an artificial climatological atmosphere. This surface warming is the result of a side effect of climatological averaging on winds where fast varying synoptic weather systems are filtered out, strongly reducing upper ocean vertical mixing and turbulent air-sea fluxes. These results illustrate the key role played by thermodynamical ocean feedbacks on the atmosphere for the development of an oceanic state of equilibrium.

In the climatological scenario, the system reaches a new balance for which the warmer ocean surface induced by weak ocean vertical mixing is balanced by increased outgoing longwave radiation. This balance is quite different from the equilibrium reached in the traditional approach (where the atmospheric state is prescribed). In the latter case, the ocean vertical mixing remains weak, but the effects of the climatological winds on the turbulent air-sea fluxes are balanced by an increased contribution of the difference between the warming ocean and the prescribed atmosphere. The turbulent air-sea fluxes are strengthened and the atmosphere controls the surface ocean dynamics by damping the surface warming tendency. However, this 'traditional' approach relies on the unrealistic assumption of an infinite heat capacity for the atmosphere, whereas the ocean is more appropriately approximated as the slow climate component since its heat capacity is much larger than that of the atmosphere. Those results suggest that the use of an atmospheric boundary layer model rather than a prescribed atmosphere when decoupling an ocean model from the atmosphere is a more suitable strategy to better represent the physics of the air-sea interactions.

To isolate the oceanic dynamics from the low-frequency atmospheric forcing when an ocean model is coupled to an atmospheric boundary layer model, one thus needs a wind product that does not contain any interannual and longer variability but which ac--11-manuscript submitted to Geophysical Research Letters counts for the fast varying winds. Last, a preliminary experiment driven by a 'normal' year strategy [START_REF] Large | Diurnal to decadal global forcing for ocean and sea-ice models: the data sets and flux climatologies[END_REF]) exhibits promising results: The oceanic state that develops under such a forcing stays in better agreement with the fully varying experiment, and atmospheric temperatures exhibit low-frequency variability which feeds back onto ocean surface dynamics. We conclude that, combined with a normal year forcing strategy, the use of an atmospheric boundary layer to drive ocean-only models for climate oriented studies is very attractive.

manuscript submitted to Geophysical Research Letters

  gust 2003 to July 2004. This experiment is run for 5 years only. Initial conditions are common to all experiments, and are derived from a 1 12 • global ocean-only simulation (cf Supporting Information).

  1 the dry atmospheric adiabatic lapse rate and h = 10 m the height at which turbulent air-sea fluxes are computed. Fig. 3 (right panel) show the sensible heat as a function of the two main contributing factors, i.e. the scalar wind speed |u| and the air-sea temperature difference (SST -T a ). As a response to a weaker wind variance in AML CLIM, there are no winds stronger than 5 m s -1 (top right panel). However, for wind speed weaker than 5 m s -1 , the sensible heat fluxes in AML CLIM remain weaker than those obtained under fully varying winds, suggesting that the changes in air-sea fluxes are not only driven by the weaker climatological wind speed |u|. The other parameter that contributes to the strength of the sensible heat fluxes is the air-sea temperature difference SST -T a .

  ter 5 months with a new SST about 8 • C warmer than for the fully varying wind experiment. The upward longwave radiation is 40-50 W m -2 stronger in the climatological wind experiment, which balances about 80% of the -60 W m -2 time mean difference in turbulent heat fluxes induced by the weakly varying climatological winds. The net airsea heat fluxes are of comparable amplitude in the two experiments, preventing the SST -6-manuscript submitted to Geophysical Research Letters difference to be much larger than 8 • C. After the 5 months of initial transition, the model slowly drifts toward its new state of equilibrium with an SST trend of about +0.25 • C/yr.

  Geophysical Research LettersThe large reduction in mixed layer depth in AML CLIM is observed all over the domain, where the maximum depth of the mixed layer computed by the KPP parameterization is about 3 to 4 times shallower North of 20 • N (Fig.1, bottom panels). This spatial pattern resembles the wind variance (top panels). In fact, in AML FULL, the high frequency wind variance induces a vertical velocity shear ∂ z u in the upper layers, that destabilizes the ocean: the Richardson number R i = N 2 ∂zu (with N 2 the buoyancy frequency) decreases, and ultimately falls below the critical value R crit. i = 0.3 used in our configuration. The vertical structure of the ocean is thus unstable to Kelvin-Helmholz shear instability, the leading process driving ocean vertical mixing for such low R i[START_REF] Mack | Richardson number and ocean mixing: Towed chain observations[END_REF]. In AML CLIM by contrast, the vertical velocity shear is much weaker in response to the weaker high frequency variance of the climatological winds, and the ocean is more stable. If less mixing occurs in the upper ocean, the surface heat fluxes induce a fast warming of the upper ocean.

  Geophysical Research Lettersthe two experiments more relevant for the attribution of the origin of low-frequency oceanic variability.

  regional configuration (same ocean model formulation coupled to CheapAML and driven by the same 'normal' year forcing). In this high resolution experiment, atmospheric temperatures computed by the atmospheric boundary layer model exhibit variability at time scales longer than one year (Fig. S4, left panel). This low-frequency atmospheric variability is particularly strong downstream of Cape Hatteras and along the North Atlantic current (Fig. S4, right panel). This is indicative of a low-frequency atmospheric variability driven by ocean processes which is obviously missing when atmospheric temperatures are prescribed with a seasonally repeating cycle. Such a low-frequency atmospheric variability feeds back onto the ocean, enhancing SST variability at low frequency. This is illustrated on Fig. S4 (right panel), where yearly averaged SST standard deviation is compared between this high resolution simulation and a companion simulation driven by prescribed 'normal' year atmospheric forcing. Although this feedback weakens SST variability in localized regions, the low-frequency SST variability is larger almost all over the domain with a pattern that largely replicates the pattern indicated by atmospheric temperature variations. Along the North Atlantic current, this increase is of about +0.3-0.4 • C and contributes to 20-30% of the ∼1.5 • C total SST low-frequency variability of this region. These preliminary results are very encouraging and highlight the benefits of using an atmospheric boundary layer model to drive ocean-only models in the context of climate studies. It could for instance bring new insights to the ongoing debate on the origin of North Atlantic climate variability

Figure 1 .

 1 Figure 1. (Top) Seasonal standard deviation σ [m s -1 ] of the wind speed ||u|| = √ u 2 + v 2 for the fully varying (left) and the climatological (right) winds. (Bottom) Maximum depth of the mixed layer [m] computed by the KPP parameterization during the first year of simulation for the AML FULL (left) and the AML CLIM (right) experiments.

Acknowledgments

We thank Camille Lique for a constructive discussion and references. We thank Bernard Barnier and its collaborators for providing us the Drakkar Forcing Sets data and the expertise for using them. This work was supported by NSF Grant OCE-1537304. Data used in this study are available at http://ocean.fsu.edu/ ~qjamet/share/data/clim wind GRL2019/.