Christine Michel
email: christine.michel@univ-poitiers.fr

Laëtitia Pierrot
email: laetitia.pierrot@univ-poitiers.fr

Towards Modelling the Technology Integration in Elementary School. A Diachronic Study of Teachers' Digital Practices During and After Covid-19 Lockdown

Keywords: Teaching Practices, Technology Integration, Digital uses, Adoption Model

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The teacher plays a decisive role in the learner's success, through his or her choice of teaching method and ability to manage the class [START_REF] Hattie | Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement[END_REF]. Teaching methods include verifying the learners' understanding regularly or explicating the course's structure for instance. The quality of classroom management is reflected by continuous supervision of the class or by providing an emulation system to reinforce certain student behaviours. More generally, these teaching practices describe activities implemented to target specific knowledge for learners. The introduction of technology into the classroom transforms these teaching practices. In France, like in other countries, introducing technology into the class is part of an institutional prescription: since 2013, "elements of digital culture" appear among teachers' expected skills. Teachers must mobilize them to vary didactic content and evaluation format and modalities while contributing to learners' digital skills development.

In this context, studies on the integration of technology in schools focus on teaching practices with technology. We conducted a literature review and observed diverse ways of analysing these practices. First, teaching practices can refer to tasks or activities mediated by digital tools (1.1) or to the use of digital resources (1.2). Furthermore, the recent context related to Covid-19 has contributed to a renewal of the issues related to the integration of technology in schools (1.3). In terms of methods, two main approaches exist (1.4): a descriptive approach, generally associated with qualitative research methods, which complements a rather quantified and modelling approach. Our previous contribution consisted in proposing a digital integration model while considering teachers' professional activity in primary and secondary schools while homeworking during the first lockdown of 2020. In this paper, we aim to start from this model to determine how teaching and digital practices evolved, after the 2020 lockdown. Following the presentation of our literature review and our model in this section, we present the study we conducted in 2021 and the main results we obtained in the next ones.

TEL activities in pedagogical practices

We apprehend the role and place of technology in teaching or learning activities using a theoretical framework built on the activity theory [START_REF] Davydov | The content and unsolved problems of activity theory[END_REF] completed by the contributions of the instrumental approach [START_REF] Rabardel | From computer to instrument system: a developmental perspective[END_REF] on the one hand, and the process described by the didactic triangle [START_REF] Augustsson | Teachers' Leadership in the Didactic Room: A Systematic Literature Review of International Research[END_REF] on the other hand. Thus, the introduction of a technical object, such as a digital resource, a website, an application, or a service in a pedagogical situation mainly fulfils three educational functions: training on basic digital skills, accessing and searching for information or supporting a learning activity. For this article, we focus on the third function. 574 Belgian elementary school teachers had their practices studied and classified through a cluster analysis [START_REF] Tondeur | Exploring the link between teachers' educational belief profiles and different types of computer use in the classroom[END_REF]. For this purpose, the authors differentiated the declared teaching practices according to "traditional" or "constructivist" teaching methods and obtained four profiles: teachers who declare both traditional and constructivist practices, with high intensity (cluster 1) or low intensity (cluster 4), those who have rather traditional (cluster 3) or rather constructivist (cluster 2) practices. By crossing these profiles with the reported digital uses, they observed that teachers with constructivist practices have greater use of technology. Chuang et al. [START_REF] Chuang | A structure equation model among factors of teachers' technology integration practice and their TPCK[END_REF] conducted a study on technology integration among 320 Taiwanese primary and secondary school teachers. In this study, integration depends primarily on internal factors, specifically teachers' perceptions of the effects of technology on student learning. In addition, participants chose to integrate technology or not according to how these technologies aligned or not with their practices.

Spiteri et al. [START_REF] Spiteri | Literature Review on the Factors Affecting Primary Teachers' Use of Digital Technology[END_REF] also examined the factors explaining technology integration in primary teachers' practices, through a literature review that includes 27 studies from 2010 to 2016. From this work, they elaborated a conceptual map with four main dimensions.

The first identified dimension relates to the school culture, which favours the development of digital practices when the school allows and supports collaborative work, provides training time for teachers, and integrates projects with technology on a local scale. The second dimension is teachers' technology knowledge: which technology, when to use them and why, based on the knowledge of themselves, their students, and the technology. In addition, the technology integration into their practices depends on their teaching experience: longer teaching experience contributes to developing more technical knowledge and therefore using it more optimally. The third dimension focuses on teachers' attitudes toward digital use. This dimension focuses on beliefs and perceptions of being effective when using technology. The literature review conducted by the authors shows that these factors do not only depend on the availability of equipment, but also on the importance they attach to it to have beneficial effects on their students (in terms of motivation or academic success for example). The fourth and final dimension concerns teachers' skills. To develop the use of technology, the studies cited in the literature review point to their ability to pick constructivist or student-centred pedagogical approaches, particularly through project-based activities, thus echoing the results cited above [START_REF] Tondeur | Exploring the link between teachers' educational belief profiles and different types of computer use in the classroom[END_REF][START_REF] Chuang | A structure equation model among factors of teachers' technology integration practice and their TPCK[END_REF].

In the French context, Dioni [START_REF] Dioni | Métier d'élève, métier d'enseignant à l'ère numérique[END_REF] notes that there is an "active" minority of teachers who develop their practices to reduce possible inequalities between students. Moreover, there is a distinction in teachers' practices between "digital" practices, relating to the perceived expectations that the school institution has for them, and "personal" practices, which they carry out outside the institution and of which they are not always aware [START_REF] Epstein | A statistical analysis of French teachers' blogs: beyond institutional perspectives Some changes in the teaching profession made visible by the study of their blogs[END_REF]. This tension between institutional (and normative) practices and other personal practices also appears while using digital resources.

Use of digital resources

Digital resources can include static or interactive content. They describe resources that teachers use or transmit in or outside the classroom [START_REF] Ratompomalala | Quelle gestion des ressources éducatives par les enseignants de sciences ? Questions Vives[END_REF]. Resources include institutional material resources (or curriculum materials), which comply with the curriculum imposed by the educational institution, and those personally produced by teachers (teacher materials) [START_REF] Reverdy | Du programme vers la classe : des ressources pour enseigner[END_REF]. As with the factors influencing the integration of technology into practice, strong links exist between teachers' beliefs and conceptions (what they think of their role, their mission), their disciplinary knowledge (and their freedom to follow the curriculum or not) and the use they make of institutional resources: these decisions are part of their professional development, and refer to their "sense of professionalism", their ability to adapt and improvise [START_REF] Mars | Professional standards, teacher careers and the enactment of professional judgement : an exploration of the discourses[END_REF]. Teachers mobilize resources inherited from their initial training or more experienced colleagues [START_REF] Diekema | The notion of relevance in teacher information behavior[END_REF] and "raw" resources extracted and collected from sites or manuals or proposed by groups to build up their corpus of resources.

In Chinese rural schools [START_REF] Wang | Connecting rural schools to quality education: Rural teachers' use of digital educational resources[END_REF], the authors have observed widespread use of "traditional" resources (digital or multimedia training aids) and a minority of "innovative" resources (video, specialized software for example). Their analysis, based on a twolevel model, leads them to conclude that the use of digital resources can be explained mainly on an individual level (the teacher): 80% of the total variance is attributed to intra-individual differences (mainly age, attitude towards the use of resources, teachers' prior knowledge and teaching experience). In this way, contextual (school) factors are less important. The authors, therefore, recommend considering individual teacher characteristics (or more directly taking teachers into account in digital plans) to facilitate the integration of digital resources into teaching practices.

The Covid-19 context

School closures imposed by the Covid-19 health context led to numerous studies examining the experience of distance learning motivated by educational continuity. In Scotland, the practices of some 60 primary school teachers were followed from March to June 2020 through in-depth interviews [START_REF] Brown | Technology as Thirdspace: Teachers in Scottish Schools Engaging with and Being Challenged by Digital Technology in First COVID-19 Lockdown[END_REF]. The participants of the study expressed the feeling of a certain pressure to offer a wide range of digital services, which placed them in a constant search for new tools.

In Spain, the activities of 1403 primary and secondary school teachers during lockdown were collected through a questionnaire [START_REF] Pozo | Teaching and Learning in Times of COVID-19: Uses of Digital Technologies During School Lockdowns[END_REF], distinguishing them according to whether they were part of traditional or constructivist pedagogical approaches and whether they targeted the acquisition of procedural, verbal or behavioural knowledge or their evaluation. Their analysis shows a predominance of traditional type activities, mainly conducted by teachers with little teaching experience; these activities mainly target the acquisition of verbal and behavioural knowledge. Based on these results, they established 4 teacher profiles: the group of "passive" teachers whose activity with technology is the least intense, and mainly according to a traditional approach, the group of "active" teachers, whose activity is more important than that of the passive teachers, still according to a mainly traditional and minority constructivist approach, the "traditional" teachers whose activity is equivalent to the previous group but with a more marked predominance towards traditional activities and the group of "interpretative" teachers whose activity is the most important and mobilizes both traditional and constructivist approaches. Primary school teachers were over-represented in the first group.

In the British context, two studies have examined the resources mobilized during the lockdown of 2020 and 2021. The first one highlights the engagement of students which was higher when schools relied on specific resources for learning, at the school level, notably through VLEs [START_REF] Lucas | Schools' responses to Covid-19: Pupil engagement in remote learning[END_REF]. On the other hand, when comparing the 2020 and 2021 lockdowns, more active strategies implemented (including the use of video conferencing tools) could be observed during the second lockdown [START_REF] Montacute | Learning in lockdown: Research brief[END_REF].

Approaches to accounting for practices

The works cited in the previous section are divided according to whether they rely on a modelling or a descriptive approach. In the first case, as summarized by Taherdoost [START_REF] Taherdoost | A review of technology acceptance and adoption models and theories[END_REF], the studies were based on models relating to the integration of technology [START_REF] Tondeur | Exploring the link between teachers' educational belief profiles and different types of computer use in the classroom[END_REF][START_REF] Chuang | A structure equation model among factors of teachers' technology integration practice and their TPCK[END_REF][START_REF] Wang | Connecting rural schools to quality education: Rural teachers' use of digital educational resources[END_REF][START_REF] Pozo | Teaching and Learning in Times of COVID-19: Uses of Digital Technologies During School Lockdowns[END_REF][START_REF] Lucas | Schools' responses to Covid-19: Pupil engagement in remote learning[END_REF][START_REF] Montacute | Learning in lockdown: Research brief[END_REF] and mobilised surveys by questionnaire with a representative aim. In the second case, the authors use more qualitative approaches while intending to conduct more in-depth analyses of the motivations or purposes of the practices, which are less generalizable [8-10, 12, 15].

In a previous study [START_REF] Michel | VLE Limits and Perspectives for Digital Integration in Teaching Practices[END_REF], we proposed a model of technology integration that considers elementary and middle school teachers' practices related to the use of a virtual learning environment (VLE) and other digital tools based on data from a questionnaire including closed and open-ended questions and in-depth interviews on the tasks performed during the first lockdown of 2020. This integration model derives from a multidimensional classification [START_REF] Kozdras | Enter the Matrix: A Pedagogy for Infusing Technology[END_REF] to differentiate teachers' behaviours according to the main purposes they were pursuing (activity design, resource delivery, facilitation, verification, communication, and self-study).

Among the 279 primary school teachers surveyed in 2020, the main reported practices with digital tools were motivated by the objectives of resource transmission (integration level 1), to which were added objectives of design (level 2), communication (level 3), self-training and verification (level 4) and finally facilitation (level 5). Most (142/279) of the teachers interviewed are located in class 4 and class 5, with a "pragmatic" [START_REF] Rogers | Diffusion of Innovations[END_REF] use distributed between the services offered by the institution (the VLE) or not and motivated by the imperative need to remain in contact with the students during the schools' closing [START_REF] Pace | Best Practices in Middle Level Quaranteaching: Strategies, Tips and Resources Amidst COVID-19[END_REF].

Research questions

The analysis of the literature shows that different studies have highlighted changes in teaching practices in elementary school to support a learning activity with the use of digital resources and technologies. Several studies question the potential impact of the lockdown. The objective of our research is to determine how teaching and digital practices evolved in France, after the 2020 lockdown. Our first research question is to determine the levels of technology integration, based on the activities implemented by teachers at school and out-of-school (RQ1). More specifically, what is the contribution of resources found on the internet, transmitted by colleagues or the institution in the integration of TEL? Our goal is also to describe the diversity and intensity of practices in 2021. Our second research question is to explain these levels of digital tools integration (RQ2) based on the individual and contextual factors identified in the previous section. More specifically, the objective is to determine whether the educational experience during the lockdown played a role in the integration of technology in the mainstream context. More broadly, we seek to measure the quality and representativeness of our approach to analyse the dynamics of technology integration in schools (RQ3). Method. We used discretization and standardization with the scale data. We identified teachers' technology use strategies over the two time periods by averaging responses on how they performed different academic tasks. We modelled the levels of technology integration (RQ1) using a 5-level K-means classification techniqueto group teachers according to their declared practices while using technology in and outside of the classroom (TIM21) and during the lockdown (TIM20) by considering questions related to practices over these two periods. We only calculated the TIM20 classification on the 525 responses from teachers who taught remotely during the period. We chose a fivelevel classification to be consistent with the TIM scale of technology integration [START_REF] Kozdras | Enter the Matrix: A Pedagogy for Infusing Technology[END_REF]. Indeed, this TIM scale considers 5 levels: entry, adoption, adaptation, infusion, and transformation [START_REF] Kozdras | Enter the Matrix: A Pedagogy for Infusing Technology[END_REF]. A matrix describes, for each level, the possible uses of technologies according to the type of learning (active, collaborative, etc.) proposed by the teacher. The TIM matrix does not consider the teacher's administrative and preparation activities. We will consider them as communication, information and design activities [START_REF] Michel | VLE Limits and Perspectives for Digital Integration in Teaching Practices[END_REF]. We performed the calculation of K-means on the normalized values. We ordered the obtained classes based on empirical studies on traditional and innovative behaviours identified in the literature.

Study on technology integration

In addition, we performed an analysis of the covariance (0.05 level of significance) between the TIM21 classification and other variables to identify if there were any explanatory factors (RQ2). The variables considered were: 8 personal variables, the 29 context variables, the practices in 2019 and 2020 (32 variables), and 29 experience variables during the first confinement. We identified a total of 18 variables considered significant and calculated mean values by integration levels for them. We used Excel and XLStat to perform all statistical analyses (bivariate or multivariate analyses).

Results

3.1

The current level of technology integration (RQ1)

Tables 1 and2 show the ratio of teachers who performed different practices during the 2020 lockdown and in normal work mode, according to the TIM20 and TIM21 integration levels and all levels combined. Thus, a value of 1 means that all teachers at that level used that practice. Traditional (resp. constructivist) activities are shown in purple (resp. blue). The communication (resp. information and design) activities are presented in orange (resp. black).

Table 1. Percentage of activities during the lockdown according to the technology integration levels TIM20 and TIM21.

Table 2. Percentage of activities in regular context according to the integration level TIM 21.

According to the TIM20 classification, the practices reported during the lockdown with technology are of the "traditional" type with the transmission of resources and the use of online resources for all levels. These practices are the more accessible ways to integrate technology tools. The level of integration is distinguished according to the mode of follow-up (by phone for class 1 and by email for class 2), the type of resources used for the design (online resource for class 3, institutional for class 4 and self-produced for class 5). These differences are less visible in 2021 with a more homogeneous behaviour at all levels which means that these practices are becoming more widespread. The strongest progression in 2021 is online coaching, which can be considered as an adaptation of practices over the period. Constructive activities such as virtual classroom facilitation or the design of personal resources are progressing but remain low. These practices are being adopted. The use of institutional resources will decrease in 2021 to the benefit of resources created by teachers.

The integration of technology tools is quite segmented in 2020 (see Table 1) with specific choices for each class (identifiable by 0's and 1's on some lines) whereas it is more inclusive and cumulative in 2021: the technologies integrated by class 2 are those of class1 plus others, etc. In the regular context (see Table 2), the most developed activities are "traditional" learning activities in the classroom: whole class or individual resource presentation and information retrieval. Technology tools are then used more and more according to the TIM level for activities outside the classroom: designing scenarios or digital resources, communicating with parents or other teachers and administrative tasks (class 2), evaluating students, and improving personal resources (class 3), self-training through internet research or collaboration between colleagues (class 4), monitoring and correcting students' work (class 5). Teachers in classes 4 and 5 also use technology for classroom activities for constructivist activities: exercise, individual and collective production of documents, communication between students (class 4), and programming and educational games (class 5). Uses outside of the classroom follow a regular progression. On the other hand, uses in the classroom, such as collaborative and constructivist TEL uses, are stopped for classes 1 and 3. Further studies must be done to understand why these practices can't be regularly adopted. Uses of exercisers and programming software seem to be good leverage for new teaching practice transformations.

Explanatory factors

Of all the variables tested, only 18 variables were significant to explain the composition of the TIM integration classes21: 5 items were related to the added value of technology, 4 items to the context (the school identification, the fact that the school equipped the teacher with a computer and the classes with peripheral devices, and that the teacher himself had devices) and 9 items to the experience during the lockdown (previous experience, integration level TIM20, reorganization of the work at school and professional isolation). These variables are marked in bold in Table 1 and Tables 345.

Personal variables. Table 3 shows the mean values for the perceived usefulness of technology, overall ("benefits of technologies") and for different educational purposes.

Table 3. Average score attributed to technology value according to the TIM21 level.

All teachers feel that technology is useful (0.87/1) especially for improving the quality of documents (0.8) and openness to the world (0.71). Overall, in the higher TIM21 levels, the feeling of usefulness is greater, which corroborates the link between the feeling of usefulness and the uses. More specifically, 5 criteria play a role in integration. Some are shared by all classes, such as training students in technology, while others are mainly identified by class TIM21-5, such as facilitating group or homework, improving evaluation or stimulating creativity. With averages of 0.68, 0.44 and 0.38, it seems quite easy to convince teachers on the first 3 criteria (train students, facilitate work at home or in a group) by giving them examples of uses. The last two (creativity and evaluation) seem to be further away from the teachers' values and practices.

Contextual variables. The level of equipment is relatively similar for all teachers. However, they feel that they are better equipped to work at home than at school. The fact that the school provides the equipment is a factor in technology integration, mainly concerning peripherals devices: a printer and hard drives at home and an interactive whiteboard (IWB) at school. In only 23 schools out of the 94, the technology integration exceeds the level TIM21-4 in a significant way. Further study is needed to understand the reasons for this by analysing the school culture [START_REF] Dioni | Métier d'élève, métier d'enseignant à l'ère numérique[END_REF].

Table 4. Average score attributed to equipment according to TIM21 integration level.

Experience variable. Several practice variables had a significant impact on technology integration: uses before COVID (in bold in Table 5) and activities during lockdown (in bold in Table 1). Using technology before COVID favours integration with 0.76 and 0.88 in TIM21-4 and 5. As described earlier, having carried out in 2020, the traditional type of training activities (sending homework, prescribing resources found on the Internet) consolidated carrying out traditional activities in 2021 but did not allow the introduction of constructivist teaching activities in the classroom. On the other hand, the fact that teachers were designing their own resources in 2020 had an impact on out-ofclass use: they found it easier to search for information on the Internet or to communicate with other teachers. Similarly, having accompanied students on the phone or by email in 2020 helped the teachers in 2021 to follow students online.

Unlike the studies cited by Spiteri et al. [START_REF] Spiteri | Literature Review on the Factors Affecting Primary Teachers' Use of Digital Technology[END_REF], skills did not impact technology integration. Teachers report being poorly trained (0.25) but having a proficient level of technical or teaching skills (resp. 0.65 and 0.69) and not having suffered from a lack of skills in 2020 (0.32 and 0.03) while having built useful skills during this time (0.86).

The professional isolation linked to the lockdown and the changes induced in the way of working at school have also significantly influenced the integration of technology, especially for classes 3 and 4 (Table 5a). Overall, teachers believe that the way they work at school has changed (Table 5b). Teachers communicate more with parents (0.81 and 0.73). To a lesser extent, they share their resources and practices more (resp. 0.63 and 0.67) and exchange with each other (0.56, 0.44, 0.40) or help each other (0.40). Some behaviours are specific to class 5 teachers: they engage in more collaborative practices with joint preparation activities (0.67), which significantly impacts technology integration, and they participate in virtual teacher communities (0.63).

Table 5. (a) Average score attributed to experience according to TIM21 integration level and (b) focus on "change at school" variable

Discussion

Emerging student-centred approaches over the period. To answer the first research question (RQ1), our study shows that overall, teachers have greater use of technology in ordinary times. Considering practices' nature and evolution, three groups appear: stabilized practices, emerging ones, and underdeveloped ones. Stabilized practices, mainly related to "traditional" pedagogical approaches: communicating and preparing/planning/designing activities outside the class and, disseminating resources in the classroom. This result is consistent with similar studies cited above [START_REF] Tondeur | Exploring the link between teachers' educational belief profiles and different types of computer use in the classroom[END_REF][START_REF] Chuang | A structure equation model among factors of teachers' technology integration practice and their TPCK[END_REF][START_REF] Mars | Professional standards, teacher careers and the enactment of professional judgement : an exploration of the discourses[END_REF]. Stabilized practices are, most of the time, combined with diversified emerging practices enhanced by the lockdown: tasks in relation to resource work, evaluation/follow-up and communication with the school. In 2021, teachers used few institutional resources and more resources shared by peers, found on the Internet or made by themselves. We need to examine whether containment has helped in setting up a new framework that limits institutional/normative "pressure" [START_REF] Dioni | Métier d'élève, métier d'enseignant à l'ère numérique[END_REF][START_REF] Epstein | A statistical analysis of French teachers' blogs: beyond institutional perspectives Some changes in the teaching profession made visible by the study of their blogs[END_REF]. Finally, underdeveloped practices include the use of educational games, communication and collaboration activities and we must analyse if this observation falls under the pragmatism approach identified in Spanish primary school teachers [START_REF] Pozo | Teaching and Learning in Times of COVID-19: Uses of Digital Technologies During School Lockdowns[END_REF]. Different dynamics of technology integration can be observed. In classes 1 and 3, the teachers prefer to integrate technology first in activities that do not directly involve the students (preparation of lessons, communication with parents, administrative tasks) and then in activities that take place in the classroom. Class 1 is a group with a "traditional" profile [START_REF] Pozo | Teaching and Learning in Times of COVID-19: Uses of Digital Technologies During School Lockdowns[END_REF] characterized by low activity while group 3 attaches a lot of importance to the preparation of material and is similar to a "reproductive" profile [START_REF] Pozo | Teaching and Learning in Times of COVID-19: Uses of Digital Technologies During School Lockdowns[END_REF]. Classes 2, 4 and 5 are "interpretative" [START_REF] Pozo | Teaching and Learning in Times of COVID-19: Uses of Digital Technologies During School Lockdowns[END_REF]: teachers use traditional and constructive practices (i.e. student-centred approaches) according to the situation. Class 4 performs more selftraining to diversify the modes of implementation, they can be described as "interpretative explorers" while class 2 renews themselves less and are rather "interpretative followers". Class 5 uses technologies for more complex practices such as programming and are "innovators". Unlike the innovation curve, which is bell-shaped, the curve of technology integration in schools (see Figure 1) follows a horizontal asymptote. The traditional group large. To make this group evolve, it is necessary to train them mainly in the practices of groups 2 and 3.

Fig. 1. The curve of technology integration in schools [START_REF] Rogers | Diffusion of Innovations[END_REF] We identify two leverage effects that should be considered. First, it is essential to offer a limited and rationalized range of technology to teachers, who in any case will concentrate on those they consider most suitable for them and their students [START_REF] Chuang | A structure equation model among factors of teachers' technology integration practice and their TPCK[END_REF][START_REF] Spiteri | Literature Review on the Factors Affecting Primary Teachers' Use of Digital Technology[END_REF][START_REF] Wang | Connecting rural schools to quality education: Rural teachers' use of digital educational resources[END_REF][START_REF] Brown | Technology as Thirdspace: Teachers in Scottish Schools Engaging with and Being Challenged by Digital Technology in First COVID-19 Lockdown[END_REF]. For this reason, we recommend involving teachers as much as possible in the choice of technology and providing design training for pedagogical activities. Second, the stabilization and emergence of "personal" rather than institutional practices mark a milestone in the professional identity of teachers [START_REF] Mars | Professional standards, teacher careers and the enactment of professional judgement : an exploration of the discourses[END_REF]. It appears that lockdown has opened up the possibility for more transfers of practices developed outside the classroom. To maintain this openness, institutions should recognize and value the activities of teachers who deviate from the normative framework by encouraging peer sharing during in-service training.

Factors explaining technology integration (RQ2).

Our results are in line with the work on the perceived usefulness of technology that precedes its actual use [START_REF] Chuang | A structure equation model among factors of teachers' technology integration practice and their TPCK[END_REF][START_REF] Dioni | Métier d'élève, métier d'enseignant à l'ère numérique[END_REF]. Referring to the traditional/constructivist classification of Tondeur et al. [START_REF] Tondeur | Exploring the link between teachers' educational belief profiles and different types of computer use in the classroom[END_REF], teachers are aware that technology is useful in general but not to support constructive learning or train students in digital skills. Our study shows that skill variables do not impact technology integration, which contrasts with previous work [START_REF] Spiteri | Literature Review on the Factors Affecting Primary Teachers' Use of Digital Technology[END_REF]. Teachers reported having been poorly trained, but still having good technical and pedagogical skills. They declared that they had learned during the COVID, that they had not experienced a lack of skills, yet they only partially integrated them into their practices, mainly for traditional activities. An incorrect self-evaluation of their skills can explain this paradox: having insufficient training, they consider that the personal efforts made to integrate technology are adapted. It is therefore essential to provide teachers with examples of constructive practices with technology to help them identify their limits in terms of technical and pedagogical skills and to encourage the implementation of these practices. In addition, it would be interesting to accompany them in a professional certification such as the PIX 3 , as it is required for students.

We believe that the dissemination of information is not a highly effective way to raise teachers' awareness of the added value of technology or the implementation of practices. Teachers are much more sensitive to direct communication with expert teachers, present in schools or in online communities. Thus, workshops or awareness-raising would be much more effective in supporting digital-related changes, in particular, integrating more constructive practices in the classroom. The context in which technology is deployed also influences the integration of technology, mainly the availability of equipment: to promote this integration, it seems necessary to systematically provide teachers with personal computers so that they can use them at home. In this way, the development of practices in and out of the classroom [START_REF] Ratompomalala | Quelle gestion des ressources éducatives par les enseignants de sciences ? Questions Vives[END_REF] can be facilitated, as well as the work of monitoring and developing effective resources [START_REF] Reverdy | Du programme vers la classe : des ressources pour enseigner[END_REF]. Classrooms should also be systematically equipped with broadcasting and interaction devices such as IWBs or visualizers to match the most common activities of primary school teachers.

Analysis of our approach to measuring TEL integration. To answer the third research question (RQ3), our approach, which combines a classification of practices and an analysis of the covariance, allowed us to see how teachers deploy strategies to integrate these technologies into their practices both outside and inside the classroom. In addition to observing an intensification of its usage that increased between 2020 and 2021, we were able to follow the evolution and stabilization of certain practices, while identifying the factors explaining these dynamics. Although initially responding to different objectives (the previous study focused more on the use of the VLE), the study presented here complements our previous results to provide an overview of the main practices conducted among French primary school teachers. In addition, our approach allowed us to cover practices that were not necessarily included in the TIM. While the matrix focuses on practices in the classroom, the analysis of our data highlights behaviours related to uses mainly in the classroom (classes 2, 4 and 5) or outside (1 and 3). This constitutes a step forward in the analysis of teachers' activity in relation to the TEL continuum. The method can nevertheless be questioned on different aspects.

Data collection and analysis. Some variables, such as the use of software or the websites used, are not well described in this study, which is more focused on the technical means. The analysis of the "other" open-ended questions in the questionnaire should be carried out to identify the software, in particular the exercises, and the Internet resources that teachers most often choose to use. Moreover, our study highlights a lack of information about certain phenomena. The surprising results regarding teachers' self-assessment of skills suggest that these data are biased or inaccurate. To have a more accurate measure of skill levels, it would be preferable to use PIX-type certification scores, but they are not used in France. It would also be interesting to refine the questions based on the expectations of school directors or government agencies. Similarly, we have identified that some schools have specific characteristics that hinder the integration of TELs, but we do not know whether these are organizational, material or related to the socio-demographic characteristics of students and families. To continue the study, we propose to analyse the 92 complementary answers of the school directors.

Diachronic analysis of practices. Does a diachronic analysis of different practices observed show an evolution in practices? For each practice, no: some are abandoned while others emerge. It is therefore impossible to compare strictly the same practices. However, the classification method allows teachers to be grouped by class of practices and our study shows that comparing classes makes sense. Diachronic studies can accurately follow the life cycle of established practices by questioning teachers regularly about how they are carried out but can also include or eliminate others because they are innovative or abandoned. A preliminary study in selected schools, in the form of interviews and focus groups, would allow for this and for the inclusion of possibly emerging impact factors that the questionnaire could measure on a larger scale. We have conducted a series of 50 interviews with teachers, principals, parents and children. We will analyse them soon to complete the results of this study, but also to identify those new factors that could be useful to observe in other future studies.

Conclusion

We conducted a study to determine the levels of technology integration, based on the activities implemented by teachers at school and out-of-school in 2021, one year after the confinement. Through the analysis of 572 primary school teachers' responses to a questionnaire, we identify 5 classes of teacher profiles: traditional, interpretative, reproductive, explorers, and innovators. We found also that the curve of digital tools integration in school is not following the classical innovation curve. It is characterized by horizontal asymptotes representing a large group of traditional teachers. Emerging student-centred approaches are also more intense than in the classical curve. We identify 3 main factors explaining technology non-integration: a lack of value in using technology to support constructive learning, a lack of equipment especially in a classroom, and a lack of collaboration culture between teachers in school. Our study shows that skill variables do not impact technology integration, which contrasts with previous work. This is explained by a lack of professional certification in digital uses. We propose various perspectives to promote technology integration and refine the approaches to measuring TEL integration.

Context of the study and research questions addressed.

  The study is part of the French ministerial program "Territoires Numériques Éducatifs" (Digital Education Territory) launched in September 2020 in the two pilot departments of Aisne and Val d'Oise to contribute to the improvement of educational efficiency with technology in times of pandemic as well as in ordinary times1 . In this context, the objective of the study is to make a diagnosis of the evolution of teachers' digital practices. We proposed a questionnaire 2 , organized into 4 parts (Personal characteristics, Work context, Practices in 2021/2020/2019, Experience during the Home Confinement) and 108 questions, from January to February 2021 to all teachers in the two departments via their professional email address.Participants. We collected 1224 complete questionnaire responses, these include 572 primary school teachers, representing 10% of each department's total share of teachers. In the Aisne department, 133 responses (out of 1336 elementary school teachers in 2019-20) were mainly from females (114), with an average age of 40 years and 15 years of service. In the Val-d'Oise department, the 439 responses (out of 4181 elementary school teachers in 2019-20) were also mostly from females (374), with an average age of 40 and 13 years of teaching seniority.

https://www.education.gouv.fr/les-territoires-numeriques-educatifs-306176

Questionnaire :

https://pix.fr/


Ludovic Orlando
email: ludovic.orlando@univ-tlse3.fr

A genetic window into the human social past

Kinship, or what links together members of the same family, fundamentally structures the web of relationships in human societies. Over the last few centuries, ethnographers have chronicled a remarkable range of kinship systems around the world, in which blood ties can be essential to irrelevant (1). Patrilineality represents the most frequent system, with family membership solely deriving from the father's lineage. When associated with patrilocality (or female exogamy), women relocate to their husbands's native region. Such marital and residence rules can typically be deduced from historical textual sources. They remain, however, often mysterious for the undocumented deeper past. In this PNAS issue, Blöcher et al. build on recent advances in ancient DNA (aDNA) research (2) to illuminate the descent, marriage and residence practices of a pastoral community that lived in Central Asia ~3,800 years ago (3). Their work reveals a patrilineal world in which male siblings were central to the community, as well as networks of interaction connecting people across hundreds of kilometers across the steppes.

The archaeology of Nepluyevsky portrays a Bronze Age necropolis of livestock herders from the Southern Urals. With 44 skeletons deposited within 50 years at best, Kurgan 1 represents one of the largest burial mounds on site. It was the focus of the study by Blöcher et al.. Clearly, females did not have the same lives as males in this community: they had a shorter life expectancy and were not even buried there if they died at an age of 5 to 14 years. DNA preserved in the remains of 32 individuals revealed a diversity of mitochondrial haplotypes, contrasting with an almost unique Y chromosome haplogroup. Since mitochondrial DNA is inherited through mothers, and the Y chromosome through fathers, the genetic pattern possibly depicted a patrilineal, patrilocal community, integrating adult females from diverse origins while maintaining a local clan founded by a single male. The pattern observed could, however, also reflect the limited diversity of Y chromosomes available throughout the region at the time. Confirmation of patrilineality was obtained when the authors turned to autosomal genetic variation, which is inherited from both parents. There, they found that pairs of males were more genetically related than pairs of females, and that almost two thirds of the individuals tested were genetically related up to the third degree. In fact, the burial mound enclosed a genealogy spanning three generations and structured around six brothers and their wives, children and grand-children. The oldest brother in the DNA family tree had eight children when the others had three at best, and he was also the only one who reproduced with two women. This points to a higher status for the eldest son in this community. The data collected show that his female partners came from different biological families, but are silent about whether serial monogamy or polygamy was involved.

No adult lineage daughters were found on site, in line with female exogamy. Only two of the 27 males tested show no evidence of close blood ties but were related to other community members within 6-10 generations. Quite strikingly, when the researchers extended their tests to 1,000+ ancient steppe people previously analyzed, they found many unambiguous matches with Nepluyevsky community members: within 50 kilometers around, but also much farther away, in Ukraine, western Russia and as far east as China and Southwest Siberia. This demonstrates that the community was integrated into a broader Bronze Age network and provides a new credible approach for gaining fine-grained resolution into its connectivity.

Blöcher et al.'s patrilineal findings are on par with ethnographic reports for cattle-keeping societies, which accumulate wealth in the form of mobile livestock that men can easily transfer to pay the price of their bride (4). Female exogamy also protects against inbreeding by providing reproductive partners who are not close biological relatives. Interestingly, considering patrilineal kinship systems offer other narratives than just male-driven warfare for some of the previously reported patterns of past human expansion. For example, if constant competition for grazing pastures incentivized the migration of patrilineal pastoral groups, particular male lineages and more genetic ancestry would be spread through

males over large areas [START_REF] Kristiansen | Archaeology and the genetic revolution in European prehistory[END_REF][START_REF] Fürtwangler | Ancient genomes reveal social and genetic structure of Late Neolithic Switzerland[END_REF]. Such apparent signals of male-mediated genetic expansions would also develop when patrilineal farming clans move to new lands, especially when reaching areas occupied by hunter-gatherers practicing more fluid residence norms (e.g. couples residing near to either spouse's genetic kin; [START_REF] Chylenski | Patrilocality and hunter-gatherer-related ancestry of populations in East-Central Europe during the Middle Bronze Age[END_REF]).

Using aDNA to identify depositional patterns in burials is not new. After all, the way the world of the dead is organized reflects decisions made by those who buried them; it, thus, offers a mirror for the social norms in the world of the living (Table 1). Combined with enamel isotopic analyses, DNA testing can inform on mobility and diet. The non-lineage mothers identified genetically can then be proved as isotopic outsiders to formally establish female exogamy, and map their native region [START_REF] Knipper | Female exogamy and gene pool diversification at the transition from the Final Neolithic to the Early Bronze Age in central Europe[END_REF][START_REF] Mittnik | Kinship-based social inequality in Bronze Age Europe[END_REF]. Finding their non-lineage sons buried on site can demonstrate that the children they had from previous unions joined their new community. The five-generation genealogy disclosed at the megalithic tomb of Hazelton North, Britain, revealed such a case of a patrilineal Neolithic community practicing female exogamy and accepting stepsons [START_REF] Fowler | A high-resolution picture of kinship practices in an Early Neolithic tomb[END_REF]. Conversely, lineage males carrying local isotopic signatures in their 'wisdom teeth' but non-local in their first molars, which erupt earlier in life, represent individuals who spent their adolescence away but ultimately returned home as adults. Such cases of potential foster sons reinforcing alliances with other clans (4) have been suggested in the early Bronze Age communities of the Lech valley, Austria [START_REF] Mittnik | Kinship-based social inequality in Bronze Age Europe[END_REF], and amongst Bell Beaker communities from South Germany [START_REF] Sjögren | Kinship and social organization in Copper Age Europe. A cross-disciplinary analysis of archaeology, DNA, isotopes, and anthropology from two Bell Beaker cemeteries[END_REF].

So far, most aDNA studies have reported patrilineal and patrilocal systems (Table 1). The Neolithic megalithic tomb from Gurgy, France, however, reminds us that such rules were not always applied strictly, as some adult lineage daughters were buried on site and even had offspring with nonlineage males [START_REF] Rivollat | Extensive pedigrees reveal the social organization of a Neolithic community[END_REF]. One exception to patrilineality was described outside the Eurasian Holocene (which attracted most aDNA work): the pre-Columbian burial crypt investigated at Chaco Canyon was that of an elite Pueblo matrilineal dynasty, which developed a complex hierarchical polity across the American southwest [START_REF] Kenett | Archaeogenomic evidence reveals prehistoric matrilineal dynasty[END_REF]. Another striking exception was found amongst Neolithic communities from Çatalhöyük and Barcın Höyük, Anatolia, where people buried in and around the same houses appeared mostly unrelated genetically [START_REF] Yaka | Variable kinship patterns in Neolithic Anatolia revealed by ancient genomes[END_REF], which asserts the importance of social relatedness at the time.

The spatial deposition of the skeletons also holds important social clues. For example, the victims of a 4,800 years-old massacre at Koszyce, Poland were deposited in a single pit, with mothers and offspring grouped together, indicating the structural role of nuclear families for the underlying community [START_REF] Schroeder | Unraveling ancestry, kinship, and violence in a Late Neolithic mass grave[END_REF]. At Gurgy, fathers and sons were buried closer to one another than all other pairs of genetic kins were, and sub-pedigrees could almost be mapped spatially, suggesting community-level knowledge of who was buried where [START_REF] Rivollat | Extensive pedigrees reveal the social organization of a Neolithic community[END_REF]. Similarly, two chambers of the Hazelton North mainly enclosed two distinct maternal lineages. This shows that founding women could have a significant role in the collective memory, even in patrilineal communities [START_REF] Fowler | A high-resolution picture of kinship practices in an Early Neolithic tomb[END_REF].

Tracking how grave goods such as weapons, adornments and pottery, follow the DNA tree has also helped understand patterns of wealth inheritance. For example, weapons were more often deposited in the graves of lineage males than in those of unrelated males across early Bronze Age sites of the Lech valley, indicating patrilineal wealth inheritance (8). This rule was not universal: the early Bronze Age site of Mokrin, Serbia showed both high-status mothers buried with low-status sons, and vice versa [START_REF] Žegarac | Ancient genomes provide insights into family structure and the heredity of social status in the early Bronze Age of southeastern Europe[END_REF]. In the Lech Valley, the identification of a group of low-status and genetically unrelated local individuals coexisting alongside the wealthy lineage males and their wealthy non-local wives also suggested that slaves were integrated in the households [START_REF] Mittnik | Kinship-based social inequality in Bronze Age Europe[END_REF].

I can only commend that aDNA technology is increasingly applied to unveil our past social life. I, however, caution that the social experience is far more complex than what visible from biological data alone. While the sexual karyotype almost immediately invites for a binary categorization of the world, other relevant identities beyond males and females are increasingly recognized as central to peoples' identities [START_REF] Johnson | Bioarchaeology and kinship: integrating theory, social relatedness, and biology in ancient family research[END_REF]. Forcing such categories into the past because they are rather easy to map genetically (17) may risk denying essential past social realities. Similarly, ethnography provides many examples of communities in which kins are not defined according to the genealogical hierarchies (e.g. parenthood extending to uncles and aunts). Identities, including parenthood, can also be dynamic entities that keep evolving through life. Some archaeological technologies, such as high-resolution serial enamel isotopic series [START_REF] Honeychurch | The archaeology of pastoral nomadism[END_REF], and possibly epigenetic profiling of markers of social inequity [START_REF] Hanghøj | DamMet: ancient methylome mapping accounting for errors, true variants, and post-mortem DNA damage[END_REF], can help reveal important changes during the lifespan of individuals. Such techniques may help grasp a more nuanced view of the fluidity of social identities in the past. Interestingly, many studies have reported some genetically unrelated adults buried together with the larger lineage community [START_REF] Fowler | A high-resolution picture of kinship practices in an Early Neolithic tomb[END_REF]. It is essential that the whole breadth of the archaeological toolkit is applied to such individuals to refine their true social reality, and hopefully reveal more subtle embodiments of the least prevailing social norms. It is also crucial to acknowledge the necessarily over-simplistic and reduced perception of the social complexity that can be preserved in the material archaeological record to avoid developing essentialist narratives about the past.

In my opinion, future work should be applied to both the human and the non-human. For example, animal domesticates are not only life companions, biocultural forms of wealth, but also symbols of prestige. Mapping out the geographies of woman exogamy and animal exchange in pastoral groups may advance understanding of mobility patterns as reinforced alliances between larger communities (4). Furthermore, some archaeological sites document the ritual practice of animal sacrifice, which provides excellent windows into the diversity of social norms then prescribed by the entire community. Testing why the animals sacrificed were chosen -whether as genetic kins or for special age, sexual, esthetical, behavioral, or performance phenotypes that can now be predicted genetically [START_REF] Todd | Imputed genomes of historical horses provide insights into modern breeding[END_REF], or epigenetically (21)and their depositional patterns, holds considerable potential for deciphering past social practices and economical alliances [START_REF] Librado | Ancient genomic changes associated with domestication of the horse[END_REF]. When deposited as funerary offerings, they also provide exceptional opportunities to gain insight into past systems of beliefs and social representations of the after-life [START_REF] Honeychurch | The archaeology of pastoral nomadism[END_REF].

Acknowledgements

My research is supported by the European Research Council (Synergy Grant Horsepower, 101071707) and the CNRS/Université Paul Sabatier International Research Laboratory programme (AnimalFarm).

Site


Pierre Chevallier
email: pierre.chevallier@ird.fr

Rysbek Satylkanov

François Delclaux

Simon Gascoin

Bakyt Ermenbaev

Jean-François Crétaux

Issyk-Kul Lake

Tien Shan

Kyrgyzstan Pierre

Current and future water balance of a mountain subcatchment of

Keywords: Mountain water balance, snow and glacier, surface runoff, future scenarios, distributed modeling

come

Introduction

High mountain basins are key sources of runoff in many regions worldwide [START_REF] Viviroli | Mountains of the world, water towers for humanity: Typology, mapping, and global significance[END_REF].

Given the dominance of snow and ice melt, their hydrological budget is particularly vulnerable to climate change [START_REF] Barnett | Potential impacts of a warming climate on water availibility in snow-dominated regions[END_REF]. In particular, rapid ongoing and foreseen changes in the cryosphere in High Mountain Asia could have profound impacts on sensitive hydrosystems [START_REF] Immerzeel | Climate Change Will Affect the Asian Water Towers[END_REF]. Lake Issyk-Kul, an endoreic lake surrounded by the Teskey Ala Too and Kungei Ala Too mountain ranges in Central Asia, Kyrgyzstan (Figure 1), is the world's second largest high-altitude lake (1607 m a.s.l.) and one of the deepest (670 m deep) (Klerkx and Imanackunov, 2002;[START_REF] Romanovsky | The closed Lake Issyk-Kul as an indicator of global warming in Tien-Shan[END_REF]. Alongside its economic, social and heritage importance, it is also of great geographical interest because on the one hand, it is a large lake located far from any ocean and on the other hand, because thanks to thermal lifts, the lake never freezes.

Observations of the lake level over recent decades suggest that the water balance in Lake Issyk-Kul is changing due to the influence of both global climate change and the collapse of the Soviet Union [START_REF] Delclaux | Un bilan hydrologique du Lac Issyk-Kul (Kirghizstan)[END_REF][START_REF] Alifujiang | Changes in intra-annual runoff and its response to climate variability and anthropogenic activity in the Lake Issyk-Kul Basin, Kyrgyzstan[END_REF]. On the one hand, climate change modifies evapotranspiration, precipitation, and snow and ice melt. On the other hand, the collapse of the Soviet Union resulted in degradation of irrigation networks in low elevation regions [START_REF] Wegerich | Coping with disintegration of a river-basin management system: Multidimensional issues in Central Asia[END_REF] leading to a significant reduction in withdrawals, but these increased again more recently with the restoration of part of the irrigated perimeters. However, separating the contribution of local and global changes to fluctuations in the level of Lake Issyk-Kul is complex since the water budget of the lake results from interplay between surface runoff and ground-water flow in the sub-basins, including seepage of groundwater into the lake itself [START_REF] Mandychev | Groundwater in the Issyk Kul basin[END_REF][START_REF] Alifujiang | System Dynamics Modeling of Water Level Variations of Lake Issyk-Kul, Kyrgyzstan[END_REF].

Therefore, to understand the hydrological budget of Lake Issyk-Kul and potential future changes, the first step is characterizing the hydrological processes underway in areas upstream of any irrigation withdrawals. In these areas, it is also critical to accurately simulate snow and ice melt to explain variations in streamflow [START_REF] Sorg | The days of plenty might soon be over in glacierized Central Asian catchments[END_REF][START_REF] Duethmann | Attribution of streamflow trends in snow and glacier melt-dominated catchments of the Tarim River, Central Asia[END_REF]. The challenge is the lack of hydrometeorological data in high elevation regions where most snow accumulates, thus hindering the calibration and evaluation of snow melt runoff models. Scientific interest in the hydroglaciology of the Issyk-Kul lake tributaries catchments dates back to the Soviet era, but the results were only published locally (in Russian) and are not available to the international community. The present study and the one by [START_REF] Uwamahoro | Modifications to Snow-Melting and Flooding Processes in the Hydrological Model -A Case Study in Issyk-Kul, Kyrgyzstan[END_REF], in which the most recent tools and methods were used, therefore has a pioneering character, although it is important to note that data on the Kara-Batkak glacier have been published by World Glacier Monitoring Service for many decades (Zemp et al., 2021).

In this context, the Chon Kyzyl-Suu basin is of particular interest because data collected in multiple in-situ observations are available thanks to a network of stream gauges, meteorological stations as well as as mass balance surveys of Kara-Batkak glacier. These data enabled us to apply a distributed hydrological model to assess the basin water balance over a period of 10 years (2010-2020). Choosing the right model was a challenge; it had to convincingly deal with both snow-glacial processes and processes related to the water balance of a large lake, since the next step will be to extend its application to the entire Issyk-Kul lake basin. A Hydrological Distributed Snow Model (HDSM, Figure 2) was chosen because it was specifically designed for the study of large lakes and their basins (Le [START_REF] Coz | Assessment of Digital Elevation Model (DEM) aggregation methods for hydrological modeling: Lake Chad basin, Africa[END_REF][START_REF] Bastola | Temporal extension of meteorological records for hydrological modelling of Lake Chad Basin (Africa) using satellite rainfall data and reanalysis datasets[END_REF] as well as for the study of mountain processes [START_REF] Savéan | Water budget on the Dudh Koshi River (Nepal): Uncertainties on precipitation[END_REF].

In the context of climate change, we also considered it important to explore what might happen in the near future in this benchmark sub-catchment using modeling, again with a view to later extrapolation to the entire basin of the large lake. To that end, we used the resulting model settings to evaluate the impact of climate change under two standard IPCC (Intergovernmental Panel on Climate Change) scenarios that are frequently used in this type of approach: ssp2-4.5 and ssp5-8.5 (IPCC, 2021; see section 1.6). The ssp2-4.5 scenario corresponds to a "business as usual" emission pathway with moderate greenhouse gas (GHG) emissions, the ssp5-8.5 scenario corresponds to increasing GHG emissions.

The paper is organized as follows. After a short description of the model and the study area, we present the available climate and hydrological data and future climate projections. The model results are presented in four sub-sections: (i) snow and ice melt, (ii) streamflow in the upper basins, (iii) streamflow in the entire Chon Kyzyl-Suu basin (iv) future hydrological trends. Finally, we discuss the uncertainties associated with these results and the key hydrological processes across the basin.

Material and method

Model description

HDSM (Figure 2) is spatially distributed as it performs all computations on a spatial grid. The main reasons for choosing this procedure are to account for the spatial variability of climatic forcing, the geomorphological structure of basins, and the dynamics of lakes or floodplains whose flooded area can vary greatly depending on bathymetry or relief. The basin is discretized in square cells as the forcing variables, not necessarily with the same resolution. The water balance is calculated for every cell, and the surface and groundwater flows are propagated toward the basin outlet. The output variables are also spatially distributed, thereby allowing extraction of the simulated flow at any location of the basin. One of the characteristics of the model is that it is possible to have soil cells or lake cells, or a mixture of the two, characterized by a coefficient varying between 0 (cell containing 100% soil) and 1 (cell containing 100% lake). Note that in HDSM terminology, the term "soil" includes the vegetation that covers it.

HDSM is conceptual as it uses a simplified representation of the hydrological processes to compute the water balance. This approach makes it possible to limit the number of the model parameters required for each cell. The parameterizations are derived from well-established hydrological models. The soil water balance is simulated using a GR4J (French abbreviation for Agricultural Engineering,4(parameters), Daily) production function [START_REF] Perrin | Improvement of a parsimonious model for streamflow simulation[END_REF]. Snow and ice melt are computed using a degree-day method [START_REF] Martinec | Parameter values for snowmelt runoff modelling[END_REF]. As a result of water production due to the balance between precipitation, snow and/or ice melt and evapotranspiration, the water content of a soil cell is divided into surface runoff and sub-surface runoff (or drainage). Each type of runoff is modeled using a reservoir law with its own specific residence time parameter. The sum of the two fluxes is then propagated to the downstream cell according to a transfer relationship similar to the uniform flow equation, but that vary depending on the slope.

To run the model, the user must provide a physiographic description of the basin including a digital elevation model and derived products (drainage direction, depression and lake areas, slope, aspect), glacier extent and surface pattern parameters (soil and vegetation). Meteorological data (air temperature, precipitation, reference evapotranspiration and open water evaporation) must be provided at a fixed time step, in this study, daily. All input data need to be distributed over the model grid.

However, despite its advantages, the choice of HDSM has one major drawback: the surface area of the glacier remains static over time. Consequently, the results of applying the model to long time intervals need to be interpreted with caution and this is undoubtedly a limit, although [START_REF] Puschiasis | Improving Knowledge about Snow by Crossing Qualitative and Quantitative Data from the Everest Region (Nepal)[END_REF] did so in a previous study conducted in the Mount Everest region in Nepal. The limits of doing so in the present study are addressed in the discussion.

Study site: Chon Kyzyl-Suu sub-catchment

The Issyk-Kul Lake environment is characterized by a contrasted continental climate [START_REF] Delclaux | Un bilan hydrologique du Lac Issyk-Kul (Kirghizstan)[END_REF]. At the elevation of the lake, mean annual precipitation varies strongly from west (~100mm/y) to east (~500mm/y) due to the combined influence of the mountains and of the lake on atmospheric water content; the monthly distribution shows the lowest precipitation amount in winter (December to February) and the highest in summer (June to September). The monthly mean temperature varies with an amplitude of more than 20°C between January (the coldest month) and July (the hottest).

The Chon Kyzyl-Suu river (Figure 3) is a south-east flowing tributary of Lake Issyk-Kul. Its downstream reach flows through the city of Kyzyl-Suu, 30 km south-west of the main district town, Karakol. Kyzyl-Suu (named Pokrovka in the Soviet era) is home to the Tien Shan High Mountain Scientific Center (TSHMSC), which is part of the National Academy of Sciences of the Kyrgyz Republic. The TSHMSC has an old tradition of mountain hydrology and glaciology research. It runs a long-term observatory of the Kara-Batkak glacier (Central Asia section in Zemp et al., 2021) and two weather stations in the upper valley of the Chon Kyzyl-Suu river.

For the current project, two existing hydrological stations that were previously observed manually, were equipped with automatic sensors in October 2015 and with data loggers in May 2016. The stations are located on the Kachkator water course, (the name of the upper reach of the Chon Kyzyl-Suu river). The upstream station, Istok, controls the flows of the Kara-Batkak glacier, just after crossing a moraine lake, and the downstream station, Ustya, controls more than 95% of the glaciated area of the Chon Kyzyl-Suu basin.

In addition, the Kyrgyz hydrometeorological agency, (hereafter "HydroMet"), runs one weather station in the city of Kyzyl-Suu and one hydrological station, named Lesnoi-Kardon, on the Chon Kyzyl-Suu river, upstream of the irrigation water intakes located between the piedmont and the lake.

Discharge data recorded at Lesnoi-Kardon (HydroMet) are available from 2012 to 2020 but include a two-year gap (May 2015-May 2017), at Ustya (for the present study), from 2016 to 2020, with yearly frozen periods from October to March, and at Istok (present study) from 2016 to 2019, with yearly frozen periods from October to April and a gap starting in 2020, due to technical failure of the sensor.

Three different digital elevation models, (SRTM -Shuttle Radar Topography Mission, GDEM -Aster

Global Digital Elevation Map and ALOS -Advanced Land Observing Satellite), and two glacier data sets (the Randolf Glacier Inventory version 6 and the Gamdam Glacier Inventory) were tested with the aim of characterizing the basin and its two sub-basins. A preliminary analysis of these sources concluded that the combination of SRTM (http://srtm.csi.cgiar.org/srtmdata/) and RGI6 glacier data set (https://www.glims.org/RGI/) was the most appropriate for the present study.

The model grid resolution was set to 15 arcsecs (approximately 460 m) as a compromise between simulation accuracy and computing cost. In addition, the resolution of 15 arcsecs is close to that of the MODIS (Moderate Resolution Imaging Spectroradiometer; see following section) products used to evaluate the model. The characteristics of the three basins studied are summarized in Table 1.

The soil parameters in HDSM (Figure 2) are mainly descriptive [START_REF] Hagemann | Improving a subgrid runoff parameterization scheme for climate models by the use of high resolution data derived from satellite observations[END_REF][START_REF] Hagemann | Impact of the soil hydrology scheme on simulated soil moisture memory[END_REF] and were kindly provided by Hagemann for our study area. This value is applied with a calibrated formula.

The present study was conducted at a daily time step covering the period 2010-2020, i.e. 11 calendar years, or 10 hydro-glaciological years. THMSC glaciologists in Kyrgyzstan base their work on a "glacier year" that runs from October to September. Weather data came from three stations (Figure 3), the first managed by HydroMet and the two other stations by TSHMSC:

 Kyzyl-Suu (78.02°E, 42.35°N, 1 765 m a.s.l.): air temperature and precipitation, with no gaps.

 Chon Kyzyl-Suu Camp (78.20°E, 42.19°N, 2 579 m a.s.l.): precipitation, with no gaps, air temperature (mean, minima and maxima), with a few gaps; atmospheric pressure, relative humidity and wind velocity at height of 0.5 m above the ground, with many gaps between 2012 and 2020.  Gap filling (for details, see Supplemental Material, document 1). The gaps in the temperature time series were filled using elevation gradients established on a seasonal basis for winter (October to April) and summer (May to September). Gaps in precipitation were filled at Kara-Batkak weather station by regression using the data observed at Chon Kyzyl-Suu Camp.

 Spatial distribution of air temperature and precipitation (for details see Supplemental Material, document 1). Spatial distribution of temperature uses the same elevation gradient as that used for gap filling. Precipitation did not follow a linear relationship with elevation, so we used the formulae of [START_REF] Eeckman | Providing a non-deterministic representation of spatial variability of precipitation in the Everest region[END_REF].

 Computing and spatializing the reference evapotranspiration (for details, see Supplemental Material, document 2). We used the Penman-Monteith equation [START_REF] Allen | Crop evapotranspiration. Guidelines for computing crop water requirements[END_REF] to compute a time series at Chon Kyzyl-Suu Camp. Gaps were filled using a regression between observations and the Copernicus ERA5 Land reanalysis [START_REF] Munoz Sabater | ERA-Land monthly averaged data from 1981 to present[END_REF].

Finally, the parameters were calibrated through simulations using a set of random parameters generated with the Latin Hypercube Sampling method [START_REF] Mckay | A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code[END_REF].

Method

The Table 2 presents a summary of the used data and their sources.

The first step of the HDSM modeling procedure consisted in setting the three snow parameters (degree-day factor, temperature and snow depth thresholds), for use in the following operations.

Calibration consisted in optimizing the parameters by comparing the daily snow cover area (SCA) computed by HDSM with that recorded by the MODIS sensor. Parameter optimization was done at the scale of the Lesnoi-Kardon basin. Because of the lack of discharge data over a long interval in 2015-2017 and in order to be consistent with observations of the sub-catchment, calibration was based on the 2017-2020 period and validated using the period 2012-2016. The MODIS SCA was obtained from the daily Aqua and Terra MODIS snow products (MOD10A1 and MYD10A1). The two products were merged and gaps filled using the method of [START_REF] Gascoin | A snow cover climatology for the Pyrenees from MODIS snow products[END_REF].

The second step consisted in calibrating the two ice melt parameters (degree-day factor and temperature threshold). In the HDSM procedure, the remaining seasonal snow that accumulates over the glacier area is transformed into ice on October 1 st . For the seven glaciological years 2013-2020, the TSHMSC reported an average annual net mass balance of -0.704 m water equivalent for the Kara-Batkak Glacier (Zemp et al., 2021). The ice melt parameters were calibrated assuming that all glaciers in the study basin have the same average annual net mass balance as the Kara-Batkak Glacier.

After setting the snow and ice parameters, the five main HDSM parameters of flow production were calibrated based on the river discharges recorded at the Ustya hydro station, and embedding the Istok headwater basin (Figure 3). Calibration covered the period 2017-2019. The best parameter set was then used for validation over the period 2016-2020 at Ustya and the period 2016-2019 at Istok.

Applying the parameter set computed for the Ustya basin produced inconsistent results for the Lesnoi-Kardon basin. Consequently, a separate calibration/validation procedure was applied to this basin that accounted for the observed time series, and included the gap from May 20, 2015 until May 5, 2017. The period 2017-2020 was used for calibration and the period 2012-2015 was used for validation.

In addition, it should be noted that HDSM only works with time series with no gaps or in which the gaps have been filled. However, the watercourses of the headwater basins, Ustya and Istok, are superficially frozen in the winter season, making rigorous comparison between observed and simulated runoff impossible.

Future scenarios

To examine how climate change will affect the study area, we used the output of the CNRM-

CMIP6-1 (Centre National de Recherches Météorologiques -Coupled Model Intercomparison

Model) global circulation model [START_REF] Voldoire | Evaluation of CMIP6 DECK Experiments With CNRM-CM6-1[END_REF]. This was a good compromise in a study whose main aim is not to discuss the respective performances of different GCMs. Daily air temperature, precipitation and atmospheric pressure were downloaded from the Copernicus Climate Change Service (https://climate.copernicus.eu/). Calibration was performed to adapt the data sets at the Chon Kyzyl-Suu weather station site, based on the same 6-year period (2015-2020); calibration consisted of applying the parameters of the normal distribution function computed with the data of the present study to the CMIP6 data set at a daily time step.

HDSM assumes that the surface area of a glacier remains constant throughout the simulation period. We consequently restricted our climate projections to the period 2015-2060. The calibrated model was applied over both Ustya and Lesnoi-Kardon basins with the input data prepared as described above. To compute the reference evapotranspiration (ET0) with the Penman-Monteith formula, we used the method described in Supplemental Material document 2. However, wind velocities were not available from CNRM-CMIP6-1. Moreover, time series contained many long gaps that were impossible to fill. For lack of a better method, we applied a constant daily value of wind velocity equal to the mean of all values recorded 0.5 m above the surface of the ground.

Results

Present Snow melt and ice melt

Figure 4 shows the simulated snow cover area compared with MODIS data. We used 3 criteria for calibration (cal) and calibration + validation (calval):

 Nash-Sutcliff (NS): cal = 0.84; calval= 0.86  relative bias; cal = -0.002; calval = 0.026  squared NS: cal = 0.84; calval = 0.84

The calibrated degree-day factor of snow melt is 4.2 mm/°C per day. The ice melt degree-day factor is 8.2 mm/°C per day, which gives an average annual net mass balance of -0.703 m wat. eq. per year for the glaciers in the Chon Kyzyl-Suu basin, and is identical to the mean observed net mass balance of the Kara-Batkak glacier in 2013-2020 (Figure 5). However, differences are apparent between the periods 2016-2017 and 2018-2019. However, the criteria values should be interpreted with caution, because they include the "frozen periods", when discharge may occur under the frozen surface of the water course, but is not "monitored". Table 3 lists the annual values of the main hydrological variables after model calibration. The above computed net mass balance deficit of 0.703 m per year, also observed at Kara-Batkak glacier, at the Ustya basin scale (glacier area of 31.45 km²) corresponds to an ice-melt volume of 0.022 km 3 per year. This Figure is in line with the values listed in Table 3.

Ustya and Istok sub-basins

Lesnoi-Kardon basin

Applying the best parameter sets obtained in Ustya/Istok sub-basins to the Lesnoi-Kardon basin did not work satisfactorily. A new calibration of the complete basin was thus necessary, not including the results obtained for the sub-basins. The corresponding volumes of the main components of the water budget are summarized in Table 4. Comparison of tables 3 and 4 highlights huge differences in the computed ice melt volumes, whereas the glacier in the Lesnoi-Kardon basin is only 4.6% larger. These differences are discussed in the following section.

Future trends

The trends given by CNRM-CMIP6-1 are summarized in Table 5.

Based on the decade 2010-2020, the mean annual air temperature for the Ustya versus Lesnoi-Kardon basins will increase by respectively 0.81°C and 0.77°C in the decade 2050-2060 under scenario ssp2-4.5, and by respectively 1.70°C and 1.77°C under scenario ssp5-8.5.

The top part of Figure 8 shows future annual precipitation given by CNRM-CMIP6-R) with its linear adjustment in the two scenarios. Under scenario ssp2-4.5, no significant trend is visible, whereas under scenario 5-8.5, there is a decrease of 8.9% over the 40-year period.

Based on the decade 2010-2020, the mean annual reference evapotranspiration for the Ustya and the Lesnoi-Kardon basins will increase by respectively, 2.2% and 2.0% in the decade 2050-2060 under scenario ssp2-4.5, and by respectively, 7.0% and 6.5% under scenario ssp5-8.5.

The set of calibrated parameters for the Ustya basin on the one hand and for the Lesnoi-Kardon basin on the other hand, were then applied using the climate data obtained from the CNRM-CMIP6-1 for the two scenarios, ssp2-4.5 and ssp5-8.5, for the period 2010-2060 (glacier years). Table 6 and Table 7 summarize the results, which are discussed in the following section.

Discussion

Uncertainties

Beven (2016) discussed different facets of the uncertainty concept in hydrological studies and distinguished several types of uncertainty. Almost all also apply to the present study:

 Uncertainties due to observed data: this concerns the intrinsic quality and the processing of the local observed data, including filling gaps in the time series.

 Uncertainties due to spatial representation: basically, this concerns the spatialization methods used for the climate data, which originates from a small number of weather stations (3 in the present study) and on orographic behaviors [START_REF] Eeckman | Providing a non-deterministic representation of spatial variability of precipitation in the Everest region[END_REF], but also on the spatial resolution chosen, which is based on computing considerations.

 Uncertainties due to modeling: Two types of model are used in the present study: (i) representing hydrological processes: the HDSM model introduces a set of calibrated parameters, not all independent, and fixes a frame of relations between the water balance elements (Figure 2), which cannot avoid an equifinality issue [START_REF] Beven | A manifesto for the equifinality thesis[END_REF] in its "setting configuration"; (ii) assessing climate scenarios: only one Global Circulation Model is considered here, with its own quota of assumptions and internal computing methods [START_REF] Voldoire | Evaluation of CMIP6 DECK Experiments With CNRM-CM6-1[END_REF].

 Uncertainties due to missing knowledge: A key element of the water processes in the basin, groundwater flows, is not known, even though the numerous glacier deposits, screes or moraines, the flat grasslands, often containing areas of peat, and the presence of a thermal resurgence are evidence for, among others, intense groundwater fluxes, including at considerable depth. Concerning the hydrological and glaciological processes, it should be noted that two additional elements were not considered in this study: permafrost or temporary frozen soils on the one hand, sublimation in the other. This problem is similar to that of groundwater flows: no field observations are available. It should thus be considered that the frozen soil issue is included in drainage and that sublimation is included in evapotranspiration.

With the exception of local field data (meteorology, hydrology and glaciology) and remote sensing data (basically, basin physiography, snow cover dynamics and glacier extent), most of these uncertainties cannot readily be quantified in the Chon Kyzyl-Suu basin. However, all remote sensing data are subject to post-processing, which could affect their reliability.

The data provided by HydroMet, a third party of the project, require a special mention. Although the weather data are direct observations and are locally comparable with similar observations in the same context, this is not the case of the discharge data at the Lesnoi-Kardon hydrological station as we were unable to obtain information on how they were established from the water levels, meaning that the hydrological processes reported are likely, but, without the possibility to quantify a rigorous confidence level, not 100% reliable. This also implies that our discussion of future scenarios is incomplete and surprises may be in store.

Present

Snow cover area

HDSM represents the snow cover dynamics rather well (Figure 4). In their study using the SWAT model, [START_REF] Uwamahoro | Modifications to Snow-Melting and Flooding Processes in the Hydrological Model -A Case Study in Issyk-Kul, Kyrgyzstan[END_REF] found a snow melt degree-day factor of 4.3 mm/°C per day in the Barskoon basin located a short distance from the Chon Kyzyl-Suu basin, while the value calibrated in the present study using HDSM is 4.2 mm/°C per day. The similarity is remarkable, especially given the notable differences between the two approaches: modeling tools (SWAT -Soil and Water Assessment Model vs HDSM), calibration time and duration (2015 vs 2017-2020) and the size of the basins (2 165 vs 308 km²). These values are nevertheless within the range of mean values reported in the literature [START_REF] Rango | Revisiting the Degree-Day Method for Snowmelt Computations1[END_REF][START_REF] Hock | Temperature index melt modelling in mountain areas[END_REF].

Glacier dynamics

As highlighted in the description of the model in section 2.1, the dynamics of glacier extension cannot be represented with HDSM, although for a 10-year period of application, it can be disregarded. However, the representation of variations in the mass balance remains reliable. [START_REF] Brun | A spatially resolved estimate of High Mountain Asia glacier mass balances from 2000 to 2016[END_REF], assessed the net mass loss of the glaciers in the Tien Shan mountains in recent years to range from 0.6 to 1.0 m water equivalent per year, with a continuous increase since 2000, in agreement with Figure 5 and in line with results obtained at the scale of the Chon Kyzyl-Suu basin (0.7 m water equivalent per year). Barandun et al. (2020) and [START_REF] Barandun | Hot Spots of Glacier Mass Balance Variability in Central Asia[END_REF] undertook a comparable analysis, also including the net mass balance of the Kara-Batkak Glacier.

Hydrological processes

At first glance, the two models and their distinct parameter sets for surface runoff appear to offer a robust first approach to the Lesnoi-Kardon basin (Figure 7) including its embedded basins, Ustya and Istok (Figure 6), although the NS and squared NS criteria are not 100% satisfactory due to the approximate reproduction of low and peak discharges by HDSM and also to the frozen sequences.

However, this result masks significant differences reflected by anomalies for the Lesnoi-Kardon basin:

 We already mentioned the problem with the 4-or 5-times higher ice melt volume modeled even though the glaciated area is not significantly larger. This also increases the ice melt degree-day-factor from 8.2 mm/°C per day to 13.3 mm/°C per day.

 The residence time of runoff in the surface reservoir is multiplied by approximately 10, or by 2 in the subsurface reservoir (Figure 2).  High runoff coefficients are observed, sometimes greater than 1, which is not aberrant in snowy and glaciated environments, as analyzed by [START_REF] Favier | Interpreting discrepancies between discharge and precipitation in high-altitude area of Chile's Norte Chico region (26-32°S)[END_REF].

Possible explanations for this concrete situation are:  Overestimation of the observed discharges at Lesnoi-Kardon in data provided by a third party, resulting from inaccurate water level records, or when drawing the rating curve, or both.

 A huge role played by circulating groundwater that cannot be monitored in the field and is only roughly represented in the HDSM model.

 Piecemeal spatial and temporal information concerning precipitation above 3 300 m a.s.l.

The absence of additional data means it is currently impossible to satisfactorily and rigorously solve the enigma surrounding this process. Nevertheless, it should be noted that the precipitation estimated at high elevations worked correctly in the case of the Ustya and Istok basins.

Based on the above limitations, it is prudent to limit our concluding analysis to the headwater basins, which do not invite serious criticism.

Future trends

Applying future scenarios ssp2-4.5 and ssp5-8.5, as proposed by the "CNRM-CMIP6-1" datasets [START_REF] Voldoire | Evaluation of CMIP6 DECK Experiments With CNRM-CM6-1[END_REF] resulted in the annual values of the main components of the water balance presented in tables 5, 6 and 7, and for precipitation, in Figure 8. Limiting our analysis to the Ustya basin, we can make the following comments:

 Real evapotranspiration, driven by the available amount of precipitated water, will not significantly affect groundwater in the next 40 years.

 Under the two scenarios, air temperature will increase by respectively, 0.8°C and 1.7°C, and reference evapotranspiration will increase respectively, by 2.2% and 7.0%.

 Although under scenario ssp2-4, there will be no noticeable change in precipitation, under scenario ssp5-8.5 there will be an 8.9% reduction over the coming 40 years, which reaches 16.3% when only precipitation in the form of snow is taken into account (Figure 8 bottom panel) linked with increasing temperature.

 The annual volume of snow melt will decrease slightly, by respectively 3.3% and 8.8% under the two scenarios over the 40-year period. When the uncertainties inherent in this type of approach are taken into consideration, this result is comparable with the previous one.

 In contrast, under both scenarios, the increase in ice melt is slower in the first half than in the second half of the 40-year period, it reaches 25% under the ssp2-4.5 scenario and more than 100% under ssp5-8.5.

 Maximum daily means per decade (Table 7) revealed no clear trends for snow and ice melt.

 Finally, all the above-mentioned conditions increase the annual discharge by, respectively, 13%, and 28% under the two scenarios. The increase is driven by ice melt that produces an annual average excess discharge [START_REF] Radić | Glaciers in the Earth's Hydrological Cycle: Assessments of Glacier Mass and Runoff Changes on Global and Regional Scales[END_REF]. A similar increase can be observed in the daily maximum discharge per decade. But these trends and figures should be interpreted with caution, since they are based on the assumption the glaciers will still be able to supply such volumes [START_REF] Chevallier | Climate change threats to environment in the tropical Andes: glaciers and water resources[END_REF][START_REF] Chevallier | River flow regime and snow cover of the Pamir Alay (Central Asia) in a changing climate[END_REF] which is far from guaranteed. [START_REF] Duethmann | Attribution of streamflow trends in snow and glacier melt-dominated catchments of the Tarim River, Central Asia[END_REF] analyzed trends in stream flows in the Tarim basin, located south of and opposite the Issyk-Kul basin, using the WASA (Model for Water Availability in Semi-Arid Environment) model [START_REF] Güntner | Simple water balance modelling of surface reservoir systems in a large data-scarce semiarid region[END_REF]. These authors reported that glacier melt increased discharge by a factor ranging from 13% to 29% over the period 1957-2004. For a comparable duration, their figures are almost identical to ours.

Conclusion

The results reported in this paper are not only in line with existing works on the same region, but additionally underline the importance of underground circulation, although unfortunately without being able to represent and quantify it in concrete terms. What is more, the results underline the ability of a distributed conceptual model to account for the complexity of water processes in a mountain environment with a poor operational field dataset.

This study is an important step forward on the way to a full model of the entire Lake Issyk-Kul basin.

The HDSM parameters calibrated on the Chon Kyzyl-Suu basin can be extended to the other mountain water courses that contribute to the lake balance. Weaknesses and uncertainties encountered at the Chon Kyzyl-Suu sub-catchment scale should be smoothed out at the lake scale, particularly the dynamics of the glacier extension processes that could not be modeled by HDSM. It will indeed be necessary to use a larger grid resolution. It should also be noted that two additional elements require careful scrutiny at the scale of the lake: the sub-surface exchanges between groundwater and lake water, and the role played by irrigation withdrawals. Some attempts to assess the contribution of the latter are promising, based on remote sensing analysis (https://labo.obs-mip.fr/multitemp/an-overview-of-irrigation-evolution-in-central-asia-with-landsat/).

Compared with other mountain ranges where the cryosphere is crucial for the future of water resources in Europe, North America, New Zealand, and also to some extent in the Andes and Hindukush Himalaya, the Central Asian region is still poorly studied and little instrumented, despite notable attempts, in particular by Chinese research projects. This study adds to our current knowledge of the cryospheric processes but underlines the numerous uncertainties surrounding hydrological slope processes and the need for more field exploration.

Finally, this study makes it possible to envisage realistic modeling with a daily time step at the scale of the basin and simulations of the lake levels in future scenarios.

Figure captions



  Kara-Batkak (78.27°E, 42.16°N, 3 286 m a.s.l.): air temperature and precipitation, only available between May and September from 2012 to 2020. HDSM uses four types of climate data: air temperature, precipitation, reference evapotranspiration and open water evaporation. In this study, evaporation from the few local open waters is assumed to be equal to the reference evapotranspiration. The grid resolution of the spacialized climatology data is the same as the one chosen for the morphology, 15 arcsecs. The preparation of forcing involves three steps: (i) filling gaps in the time series; (ii) spatializing the temperature and precipitation data over the study basins at the modeling resolution; (iii) computing and spatializing the reference evapotranspiration.

Figure 6

 6 Figure 6 shows the observed vs HDSM discharge at Ustya and Istok, with calibration at Ustya and validation in both sub-catchments. At Ustya, we obtained the following criteria:  NS: cal = 0.65; calval= 0.56  relative bias; cal = -0.004; calval = 0.112  squared NS: cal = 0.71; calval = 0.60 At Istok, we obtained:  NS: calval= 0.66  relative bias: calval = -0.136  squared NS: calval = 0.62

Figure 7

 7 Figure 7 plots the comparison of the discharges observed at Lesnoi-Kardon and those obtained with HDSM applying the best parameter set and distinguishing calibration (2017-2020) from validation. We obtained:  NS: cal = 0.50; calval= 0.51  relative bias; cal = -0.038; calval = -0.009  squared NS: cal = 0.58; calval = 0.58

1 .

 1 Upper panel: map of Kyrgyzstan. Lower panel: map of Issyk-Kul Lake basin showing the Chon Kyzyl-Suu basin. Projection: WGS84, UTM zone 43N. 2. Flow chart of the HDSM model in the absence of a lake.. [RET = real evapotranspiration; ET0 = reference evapotranspiration; Ta = air temperature; P = precipitation] 3. Chon Kyzyk Suu River basin. Projection: WGS84, UTM zone 43N. 4. Calibration / Validation of the daily snow cover area in the Lesnoi-Kardon basin using the HDSM model. [1.Obs = MODIS product, 2. Calibration=HDSM calibration (2017-2020), 3. Validation=HDSM validation (2012-2016)] 5. Comparison of the observed annual net mass balance of the Kara-Batkak Glacier and the simulated balance for the glaciers in the Chon Kyzyl-Suu basin (Oct. 2013-Sept. 2020). The line represents the identical average of both time series. 6. Calibration / Validation of the daily discharge at Ustya and Istok hydro stations using the HDSM model. [1.Obs = observed discharge, 2. Calibration=HDSM calibration (2017-2019), 3. Validation= HDSM validation (2016 & 2020 at Ustya; 2016 at Istok)].

  Notes: data in km 3 /y, except for diff; diff is the relative difference of the decade 2050-2060 with the decade 2010-2020, not computed for Lesnoi-Kardon, due to the inconstancy observed for this basin.

		Snow melt	ssp2-4.5 ssp5-8.5	0.091	0.085 0.097	0.088 0.083	-3.3% -8.8%
		Ice melt	ssp2-4.5 ssp5-8.5	0.028	0.043 0.029	0.035 0.061	25% 110%
		Discharge	ssp2-4.5 ssp5-8.5	0.088	0.091 0.099	0.099 0.113	13% 25%
		RET	ssp2-4.5 ssp5-8.5	0.092	0.097 0.092	0.095 0.104
	Lesnoi-	Snow melt	ssp2-4.5 ssp5-8.5	0.126	0.110 0.127	0.114 0.104
	Kardon	Ice melt	ssp2-4.5 ssp5-8.5	0.096	0.115 0.103	0.126 0.198
		Discharge	ssp2-4.5 ssp5-8.5	0.208	0.203 0.202	0.206 0.272

Table 6 (

 6 Editable version) Click here to access/download;Table (Editable version);Table_6-rev2.docx

Acknowledgements and funding

The authors acknowledge collaboration with the Tien Shan High Mountain Scientific Center, especially with Nurzat Jamangulova, Danyar Saykbaev and Nurdine Sagynbaev. They also thank members of the French team who helped with the field missions, especially Muriel Bergé-Nguyen, Alexei Kouraev, Michel Le Page, Denis Ruelland and Patrick Seyler.

The authors thank Ekaterina Rets, from the Institute of Geophysics, Polish Academy of Science, for exchanges and field discussions. They are grateful to Bernard Pouyaud, scientist emeritus and former head of continental water studies at IRD for his critical reading of our paper. They finally thank the two anonymous reviewers, who helped us considerably improve our paper.

Weather data at Kyzyl-Suu and discharge data at Lesnoi-Kardon were provided by the Kyrgyz Hydro-Meteorological Agency.

The study was partially funded by the Centre National d'Etudes Spatiales (Hybiss and SWOT projects), and partially by the recurrent operational budgets of the research units involved 470 (TSHMSC, HydroSciences, LEGOS, CESBIO).

Basin