positioning theory case study

• Graduate School of Education
• Center for Literacy and Reading Instruction
• UB Directory
• Positioning Theory Conference 2024 >
• What is Positioning Theory

REGISTRATION NOW OPEN for 2022 Positioning Theory Conference July 24–27  •   Register now

July 28 to Aug. 1, 2024  •  University of Eastern Finland

What is Positioning Theory?

In 2012, Professor Rom Harré defined positioning theory as being “… based on the principle that not everyone involved in a social episode has equal access to rights and duties to perform particular kinds of meaningful actions at that moment and with those people. In many interesting cases, the rights and duties determine who can use a certain discourse mode … A cluster of short-term disputable rights, obligations and duties is called a ‘position’” (2012, p. 193).

Moghaddam and Harré (2010, p. 2) stated that positioning theory is about “how people use words (and discourse of all types) to locate themselves and others”. Further, that is “it is with words that we ascribe rights and claim them for ourselves and place duties on others” (p. 3). Positioning has direct moral implications, such as some person or group being located as ‘trusted’ or ‘distrusted’, ‘with us’ or ‘against us’, ‘to be saved’ or ‘to be wiped out’” (Moghaddam & Harré, 2010, p. 2).

VIDEO:  Professor Rom Harré speaking about the history and trajectory of positioning theory, at the inaugural event in 2015.

Positioning theory is a social constructionist approach (Slocum & Van Langenhove, 2003) that began to emerge in the 1980s primarily in the area of gender studies, including the work of Brownwyn Davies (Davies & Harré,1990a).

“Davies also drew from post-structuralist theory and feminist scholars to discuss subjectivity, storyline and narrative, all of which figure prominently in Positioning Theory. There is also a very strong connection between Davies’ interests and perspectives and those of Hollway [1984], who is generally credited with introducing “position” and “positioning” in her work on gender relations and sexuality (Van Langenhove & Harré, 1999a, p. 16), influencing the writings of Davies and Harré (1990a,b) and other positioning theorists” (McVee, Silvestri, Barrett, & Haq, 2019, p. 386).

Following the publication of work by Davies and Harré further work in developing and refining Positioning Theory has been carried out predominantly by  Rom Harré, Ali Moghaddam, and Luk van Langenhove (Harré  & Moghaddam, 2003; Harré & van Langenhove, 1991, 1999; Moghaddam, 1999; Moghaddam, Harré, & Lee, 2008); van Langenove & Harré, 1994; van Langenhove, 2017) and numerous other works.

Since the late 1990s, Positioning Theory has been seen to allow “for a very natural expansion of scale, from the analysis of person-to-person encounters to the unfolding of interactions between nation states” (Harré, Moghaddam, Pilkerton Cairnie, Rothbart & Sabat, 2009, p. 6).

Although originating in the field of social psychology it has had widespread application over the last decade or so (Moghaddam & Harré, 2010). It has especially been taken up in the field of education (McVee, Brock & Glazier, 2011, Redman, 2008) but has also included research in areas as varied as anthropology (e.g. Handelman, 2008), communication studies (Hirvonen, (2013), midwifery (Phillips, Fawns, & Hays, 2002), workplace agency (Redman, 2013), political identity studies (e.g. Slocum-Bradley, 2008), and public relations and strategic communication (e.g. James 2014; Wise & James, 2013) among others.

Davies, B., & Harré, R. (1990a). Positionings: The discursive production of selves In B. Davies (Ed.),  A body of writing  (pp. 87-106). New York: AltaMira Press.

Davies, B., & Harrè, R. (1990b). Positioning:  The discursive production of selves.  Journal for  Davies, B., & Harrè, R. (1990b). Positioning:  The discursive production of selves.  Journal for the Theory of Social Behaviour, 20 (1), 43-63.

Handelman, D (2008). Afterword:  Returning to cosmology – thoughts on the positioning of belief .  Social Analysis , 52(1): 181–95.

Harré, R. (2012) Positioning theory: moral dimensions of social-cultural psychology. In J. Valsiner (ed.)  The Oxford Handbook of Culture and Psychology . New York: Oxford University, pp. 191–206.

Harré, R., & Moghaddam, F. M. (Eds.). (2003).  The self and others . Westport, CT: Praeger.

Harré, R., & van Langenhove, L. (1991). Varieties of positioning. Journal for the Theory of Social Behaviour, 21(4), 393-407.

Harré, R., & van Langenhove, L. (Eds.). (1999).  Positioning theory: Moral contexts of intentional action  Malden, MA: Blackwell Publishers.

Harré, R., Moghaddam, F., Pilkerton Cairnie, T., Rothbart, D. and Sabat, S. (2009) Recent advances in positioning theory. Theory and Psychology, 19(1): 5–31.  doi: 10.1177/0959354308101417 .

Harré, R. and Van Langenhove, L. (1999)  Positioning Theory: Moral contexts of intentional action .  Oxford: Blackwell.

Herbel-Eisenmann, B. A., Wagner, D., Johnson, K. R., Suh, H. & Figueras, H. (2015). Positioning in mathematics education: Revelations on an imported theory.  Educational Studies in Mathematics , 89(2), 185-204.

Hirvonen, P. (2013) Positioning in an Inter-Professional Team Meeting: Examining Positioning Theory as a Methodological Tool for Micro-Cultural Group Studies.  Qualitative Sociology Review  9(4), 100-114.

Hollway, W. (1984). Gender difference and the production of subjectivity. In J. Henriques, W. Hollway, C. Urwin, C. Venn, & V. Walkerdine (Eds.),  Changing the subject  (pp. 223-261). New York: Routledge.

James, M. (2014).  Positioning Theory and Strategic Communications: A new approach to public relations research and practice . London: Routledge.

McVee, M. B., Brock, C. H., & Glazier, J. A. (Eds.). (2011).  Sociocultural positioning in literacy: Exploring culture, discourse, narrative, and power in diverse educational contexts . Cresskill, NJ: Hampton Press.

McVee, M. B., Silvestri, K. N., Barrett, N., & Haq, K. S. (2019). Positioning Theory. In D. E. Alvermann, N. J. Unrau, M. Sailors, & R. Ruddell (Eds.),  Theoretical models and processes of literacy  (7th ed., pp. 381-400). New York: Routledge.

Moghaddam, F. M. (1999). Reflexive positioning:  Culture and private discourse. In R. Harré & L. Van Langenhove (Eds.),  Positioning theory: Moral contexts of intentional action  (pp. 74-86). Malden, MA: Blackwell.

Moghaddam, F. M., Harré, R., & Lee, N. (Eds.). (2008).  Global conflict resolution through positioning analysis . New York: Springer.

Moghaddam, F. and Harré, R. (2010) Words, conflicts and political processes. In F. Moghaddam and R. Harré (eds)  Words of Conflict, Words of War: How the language weuse in political processes sparks fighting . Santa Barbara, CA: Praeger.

Phillips, D., Fawns, R., & Hayes, B. (2002). From personal reflection to social positioning: The development of a transformational model of professional education in midwifery.  Nursing Inquiry, 9 (4), 239-249.

Redman, C. (2008).  The Research planning meeting . In R. Harré, F. Moghaddam and N. Lee (Eds.),  Global Conflict Resolution Through Positioning Analysis.  Springer New York, pp. 95-112.

Redman, C. (Ed.) (2013). Planning for Science Learning Using the 5E’s: Incorporating ICT with Purpose and Confidence. In  Successful Science Education Practices: Exploring what, why and how they worked ( pp. 17-3), New York: NOVA Science publishers.

Slocum-Bradley, N. (Ed.) (2008).  Promoting conflict or peace through identity . Farnham, UK: Ashgate.

Van Langenove, L. (2017). Varieties of moral orders and the dual structure of society: A perspective from positioning theory.  Frontiers in Society, 2(9) .  http://doi.org/10.3389/fsoc.2017.00009 .  Frontiers in Sociology, 2 (9), np. doi:10.3389/fsoc.2017.00009

Van Langenhove, L., & Harrè, R. (1994). Cultural stereotypes and positioning theory.  Journal for the Theory of Social Behaviour, 24 (4), 359-372.

Wise, D. & James, M. (2013). Positioning a price on carbon: Applying a proposed hybrid method of positioning discourse analysis for public relations.  Public Relations Inquiry. doi: 10.1177/2046147X13494966, vol. 2, no. 3, 327-353.  https://journals.sagepub.com/doi/abs/10.1177/2046147x13494966

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to  upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

• We're Hiring!
• Help Center

Positioning Theory: Its Origins, Definition, and Directions in Education

2020, Handbook of Cultural Foundations of Education

Positioning Theory was originally developed three decades ago by Davies and Harré (1990) at the intersection of social and discursive psychology and feminist theories in education. It was developed as an analytic lens and explanatory theory to show how learning, and development of identity, evolves through discourse. When used as an analytic lens in education, Positioning Theory focuses researchers on examining the in and over time construction of positioning actions of teachers and students in developing episodes for learning and participating in classrooms. As an explanatory theory, Positioning Theory serves as a set of guiding principles for investigating the consequences of the discourse and the interactions of, and with, particular students and groups of students as they assume or reject particular positions or acts of positioning. Thus, Positioning Theory frames ways of examining position-positioning relationships as dynamic and developing within and across time, events/episodes, and configurations of actors, within and across social spaces in classrooms and other social contexts. The goals of this chapter are presented in two parts. The first section presents the history and development of Positioning Theory as an explanatory theory that has evolved as it has been taken up by different disciplines to examine issues of identity within particular contexts (e.g., in social and discursive psychology, management studies, nursing, and education, among others). In the second section, we present two telling case studies (Mitchell, 1984; defined later) that make transparent 1 how Positioning Theory served as an analytic lens to guide two of the co-authors of this chapter, Harris and Baker, in (re)analyzing archived records from their original longitudinal research studies to explore position-positioning relationships. The goal of these (re)analyses was to explore how Positioning Theory made visible previously unexamined processes that framed the identity potentials and performance styles of students in each site: first grade students in literacy events in Harris' study and two first-year seniors in performing public critique in an intergenerational (Grades 9-12) high school Advanced Placement studio art program (Baker, 2001).

Related Papers

Linguistics and Education

Kate Anderson

Mary McVee , Cynthia Brock

This chapter presents an introduction and overview to positioning theory as developed by Rom Harré, Bronwyn Davies, Luk van Langenove, Fathali Moghaddam and others. The chapter explores the educational affordances of positioning theory for educational researchers and particularly for those working with literacy education and teacher education.

Judith Green

International Journal of Qualitative Studies in Education

Jennifer Collett

Identities are dynamic, constantly shifting processes of self-understand- ing mediated by local and institutional repertoires, behaviors, resources and enacted through one’s positioning in practice. This definition con- siders identities as both ideas, as well as actions in terms of how the learner becomes a participant in activities. A tension in studying identi- ties is that the researcher must collect data that encompasses both observable actions and how the learner reflects on these actions. Drawing upon positioning theory, this paper presents a methodological approach to study this tension. More specifically, data from a study of emergent bilinguals in elementary school is used to understand how learners’ identities are shaped during the nascent years of school.

Positioning Theory Sociocultural Positioning in Literacy: Exploring Culture, Narrative, Discourse, and Power in Diverse Educational Contexts

This volume is the first book published in the field of education, and particularly literacy and language education, that exclusively uses positioning theory. Chapter authors use positioning theory as a guiding framework to examine teaching and learning in literacy-related contexts. These contexts include a range of literate practices, participants, and settings. Authors examine how teachers respond to multicultural texts, how adults guide children to appropriate academic discourse, how children engage in meaningful talk about texts—or avoid that talk, and how researchers write up and position themselves and their participants. Throughout the book, literacy practices, whether involving children or adults, are viewed as situated social processes contingent upon cultural contexts and the meaning-making systems used within such contexts. Each section of three chapters is preceded by framing discussion from the editors. Each section is followed by commentary from scholars in the field.

Learning, Culture and Social Interaction

Antonio Iannaccone

Angel Steadman

Developed as a socio-constructivist theory with the aim of understanding discursive construction of selves, Positioning Theory has been applied to the analysis of conversations and narratives across disciplines. This paper provides an overview of Positioning Theory developed by Rom Harré and his colleagues and describes the basic concepts and principles of the theory. By illustrating how it has been applied to studies in contexts that involve English language learners or teachers, the paper identifies ways that Positioning Theory may positively impact classroom practice and outlines areas for further research that EMI classroom practitioners can carry out. A number of practical guidelines for conducting positioning analysis are also offered.

Diane Barone

This chapter focused on the revisioning of an earlier study and a new analysis that considered the results through the use of positioning theory.

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

RELATED PAPERS

Researching Education Visually Digitally Spatially

Rick A . Breault

Noah Asher Golden

Alec MacLeod , Sara M Acevedo , Juei-Chen Chao , Claudia Moutray, PhD , Christina Olague

Conference Proceedings of the 35th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education

Alexandria Theakston Musselman

Mathematics Education Research Journal

Sandi Tait-McCutcheon

Catherine Beaton

E Beverly Young

College Composition and Communication

Phil Bratta

The Reading Teacher

Kristin N Rainville

Proceedings of FabLearn 2019

Chrystalla Mouza

Mind, Culture, and Activity

Elizabeth Hirst

margery osborne

Papers on Social Representations

Eleni Andreouli

Patrick Baert

Anna De Fina

Papers on Social Representation

Deborah Wise

Journal of Curriculum Studies

Mind Culture and Activity

Journal of the Canadian Association for Curriculum …

Julia Ellis

Educational Studies in Mathematics

Beth Herbel-Eisenmann

Aslam Fataar

Research in the Teaching of English

Jessica Zacher Pandya

Journal for Language Teaching

Nazarana Mather

RELATED TOPICS

•   We're Hiring!
•   Help Center
• Find new research papers in:
• Health Sciences
• Earth Sciences
• Cognitive Science
• Mathematics
• Computer Science
• Academia ©2024

Information

• Author Services

Initiatives

You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader.

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess .

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Original Submission Date Received: .

• Active Journals
• Find a Journal
• Proceedings Series
• For Authors
• For Reviewers
• For Editors
• For Librarians
• For Publishers
• For Societies
• For Conference Organizers
• Open Access Policy
• Institutional Open Access Program
• Special Issues Guidelines
• Editorial Process
• Research and Publication Ethics
• Article Processing Charges
• Testimonials
• Preprints.org
• SciProfiles
• Encyclopedia

Article Menu

• Subscribe SciFeed
• Google Scholar
• on Google Scholar
• Table of Contents

Find support for a specific problem in the support section of our website.

Please let us know what you think of our products and services.

Visit our dedicated information section to learn more about MDPI.

JSmol Viewer

Positioning theory in education.

1. Introduction

1.1. positions, 1.2. speech and other acts, 1.3. storylines, 2. why positioning theory.

• What you can do.
• What you do.
• What you are permitted or forbidden to do.

3. Varieties of Moral Orders and Positioning Theory

4. some applications of positioning theory in education, extending on one example: positioning theory applied to environmental discourses and education for sustainable development, author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

• Harré, R.; Van Langenhove, L. Positioning Theory: Moral Contexts of Intentional Action ; Blackwell Publishers: Oxford, UK, 1999; pp. 1–32. [ Google Scholar ]
• Bruner, J.S. Actual Minds, Possible Worlds ; Harvard University Press: Cambridge, MA, USA, 1986. [ Google Scholar ]
• Harré, R. Positioning theory: Moral dimensions of social-cultural psychology. In The Oxford Handbook of Culture and Psychology ; Valsiner, J., Ed.; Oxford University Press: Oxford, UK, 2012; pp. 191–206. [ Google Scholar ]
• Bateson, G. Naven: A Survey of the Problems Suggested by a Composite Picture of the Culture of a New Guinea Tribe drawn from Three Points of View ; Stanford University Press: Redwood City, CA, USA, 1965. [ Google Scholar ]
• Bateson, G. Steps to an Ecology of Mind: Collected Essays in Anthropology, Psychiatry, Evolution, and Epistemology ; University of Chicago Press: Chicago, IL, USA, 2000. [ Google Scholar ]
• Watzlawick, P.; Jackson, D. On human communication. J. Syst. Ther. 2010 , 29 , 53–68. [ Google Scholar ]
• Habermas, J. Moral Consciousness and Communicative Action ; Translated by Christian Lenhardt and Shierry Weber Nicholsen. Introduction by Thomas A. McCarthy; The MIT Press: Cambridge, MA, USA, 1990. [ Google Scholar ]
• Habermas, J. Theory of Communicative Action, Volume One: Reason and the Rationalization of Society ; Beacon Press: Boston, MA, USA, 1984. [ Google Scholar ]
• Potter, J.; Wetherell, M.; Gill, R.; Edwards, D. Discourse: Noun, Verb or Social Practice? In Critical Discursive Psychology ; Palgrave Macmillan: London, UK, 2015. [ Google Scholar ] [ CrossRef ]
• Butler, J. Performative Acts and Gender Constitution: An Essay in Phenomenology and Feminist Theory. Theatre J. 1988 , 40 , 519–531. [ Google Scholar ] [ CrossRef ]
• Austin, J. How to Do Things with Words ; Clarendon Press: Oxford, UK, 1962. [ Google Scholar ]
• Searle, J. The Construction of Social Reality ; The Free Press: New York, NY, USA, 1995. [ Google Scholar ]
• Fairclough, N. Critical Discourse Analysis: The Critical Study of Language ; Longman: London, UK, 1995. [ Google Scholar ]
• Fairclough, N. Analysing Discourse: Textual Analysis for Social Research ; Routledge: London, UK, 2003. [ Google Scholar ]
• McVee, M. Positioning Theory Sociocultural Positioning in Literacy: Exploring Culture, Discourse, Narrative, and Power in Diverse Educational Contexts ; McVee, M.B., Brock, C.H., Glazier, J.A., Eds.; Hampton Press: New York, NY, USA, 2011. [ Google Scholar ]
• Harré, R.; Moghaddam, F. Intrapersonal conflict. In Global Conflict Resolution through Positioning Analysis ; Springer: New York, NY, USA, 2008; pp. 65–78. [ Google Scholar ]
• Kayi-Aydar, H. “If Carmen can analyze Shakespeare, everybody can”: Positions, conflicts, and negotiations in the narratives of Latina pre-service teachers. J. Lang. Identity Educ. 2018 , 17 , 118–130. [ Google Scholar ] [ CrossRef ]
• Tirado, F.; Gálvez, A. Positioning Theory and Discourse Analysis: Some Tools for Social Interaction Analysis. Hist. Soc. Res. 2008 , 33 , 224–251. [ Google Scholar ]
• Hirvonen, P. Positioning theory and small-group interaction: Social and task positioning in the context of joint decision-making. Sage Open 2016 , 6 , 2158244016655584. [ Google Scholar ] [ CrossRef ]
• Searle, J. Speech Acts: An Essay in the Philosophy of Language ; Cambridge University Press: Cambridge, UK, 1969. [ Google Scholar ]
• Van Langenhove, L. The discursive ontology of the social world. In The Second Cognitive Revolution: A Tribute to Rom Harré ; Christensen, B.A., Ed.; Springer: Cham, Switzerland, 2019. [ Google Scholar ]
• Anderson, K.T. Applying Positioning Theory to the Analysis of Classroom Interactions: Mediating Micro-Identities, Macro-Kinds, and Ideologies of Knowing. Linguist. Educ. 2009 , 20 , 291–310. [ Google Scholar ] [ CrossRef ]
• Felix, S.M.; Ali, S. Capturing Dynamic Shifts in Learning of Mathematics Teachers in a Collaborative Setting: A Positioning Theory Perspective. Philos. Math. Educ. J. 2022 , 39 , 47–61. [ Google Scholar ]
• Harré Presentation in a Symposium in Bruges (8 July 2015). Available online: https://www.youtube.com/watch?v=CxmHTk7aYto (accessed on 20 January 2023).
• Green, J.L.; Brock, C.; Baker, W.D.; Harris, P. Positioning theory and discourse analysis: An explanatory theory and analytic lens. In Handbook of the Cultural Foundations of Learning ; Routledge: London, UK, 2020; pp. 119–140. [ Google Scholar ]
• Harré, R.; Moghaddam, F.M.; Cairnie, T.P.; Rothbart, D.; Sabat, S.R. Recent advances in positioning theory. Theory Psychol. 2009 , 19 , 5–31. [ Google Scholar ] [ CrossRef ]
• Van Langenhove, L. Varieties of Moral Orders and the Dual Structure of Society: A Perspective from Positioning Theory. Front. Sociol. 2017 , 2 , 9. [ Google Scholar ] [ CrossRef ]
• Kohlberg, L. Essays in Moral Development, Vol. I: The Philosophy of Moral Development ; Harper & Row: New York, NY, USA, 1981. [ Google Scholar ]
• Harré, R. Social elements as mind. Br. J. Med. Psychol. 1984 , 57 , 127–135. [ Google Scholar ] [ CrossRef ] [ PubMed ]
• Harré, R.; Gillett, G. The Discursive Mind ; Sage: London, UK, 1994. [ Google Scholar ]
• Popkewitz, T. Cosmopolitanism and the Age of School Reforms: Science, Education, and Making Society by Making of Child ; Routledge: London, UK, 2008. [ Google Scholar ]
• Slocum, N.; Van Langenhove, L. Integration Speak: Introducing Positioning Theory in Regional Integration Studies. In The Self and Others: Positioning Individuals and Groups in Personal, Political, and Cultural Contexts ; Harré, R., Moghaddam, F., Eds.; Praeger Publishers/Greenwood Publishing Group: Westport, CT, USA, 2003; pp. 219–234. [ Google Scholar ]
• McVee, M.B.; Silvestri, K.N.; Barrett, N.; Haq, K.S. Positioning theory. In Theoretical Models and Processes of Literacy , 7th ed.; Alvermann, D.E., Unrau, N.J., Sailors, M., Ruddell, R.B., Eds.; Routledge: New York, NY, USA, 2019; pp. 381–400. [ Google Scholar ]
• Herbel-Eisenmann, B.; Wagner, D. Appraising lexical bundles in mathematics classroom discourse: Obligation and choice. Educ. Stud. Math. 2010 , 75 , 43–63. [ Google Scholar ] [ CrossRef ]
• Anderson, D. Casting recasting gender: Children constituting social identities through literacy. Res. Teach. Engl. 2002 , 36 , 391–427. [ Google Scholar ]
• McVee, M. Positioning Theory and Sociocultural Perspectives: Affordances for Educational Researchers ; Hampton Press: New York, NY, USA, 2011; pp. 1–22. [ Google Scholar ]
• Kayi-Aydar, H. A language teacher’s agency in the development of her professional identities: A narrative case study. J. Lat. Educ. 2019 , 18 , 4–18. [ Google Scholar ] [ CrossRef ]
• Ritchie, S.M. Student positioning within groups during science activities. Res. Sci. Educ. 2002 , 32 , 35–54. [ Google Scholar ] [ CrossRef ]
• Felix, S.M.; Lykknes, A.; Staberg, R.L. Identifying the ‘Different we’s’ in Primary Teachers’ Education for Sustainable Development Discourse—A Positioning Theory Perspective. Sustainability 2022 , 14 , 13444. [ Google Scholar ] [ CrossRef ]
• Felix, S.M. Critical Thinking (Dis)Positions in Education for Sustainable Development—A Positioning Theory Perspective. Educ. Sci. 2023 , 13 , 666. [ Google Scholar ] [ CrossRef ]
• Slocum-Bradley, N. The Positioning Diamond: A trans-disciplinary framework for discourse analysis. J. Theory Soc. Behav. 2009 , 40 , 79–107. [ Google Scholar ] [ CrossRef ]
• Harré, R.; Brockmeier, J.; Mühlhäusler, P. Greenspeak: A Study of Environmental Discourse ; Sage: Thousand Oaks, CA, USA, 1999. [ Google Scholar ]
• Van Langenhove, L. Towards the Spoken World Theory: The contribution of Rom Harré to advancing social theory. J. Theory Soc. Behav. 2021 , 51 , 273–290. [ Google Scholar ] [ CrossRef ]

Click here to enlarge figure

Share and Cite

Felix, S.M.; Ali, S. Positioning Theory in Education. Encyclopedia 2023 , 3 , 1009-1019. https://doi.org/10.3390/encyclopedia3030073

Felix SM, Ali S. Positioning Theory in Education. Encyclopedia . 2023; 3(3):1009-1019. https://doi.org/10.3390/encyclopedia3030073

Felix, Sonia Martins, and Sikunder Ali. 2023. "Positioning Theory in Education" Encyclopedia 3, no. 3: 1009-1019. https://doi.org/10.3390/encyclopedia3030073

Article Metrics

Article access statistics, further information, mdpi initiatives, follow mdpi.

Subscribe to receive issue release notifications and newsletters from MDPI journals

1st Edition

The Routledge International Handbook of Positioning Theory

• Taylor & Francis eBooks (Institutional Purchase) Opens in new tab or window

Description

This handbook is the first of its kind to explore Positioning Theory. Taking inspiration from the groundwork set by Rom Harré and collaborators such as Bronwyn Davies, Fathali Moghaddam, Luk Van Langenhove, and others the book explores the emergence, historical context, and disciplinary applications of Positioning Theory and its basic precepts as a social psychological theory. This volume encompasses over 20 chapters across four sections, assimilating cross-disciplinary insights that try to understand the theoretical underpinnings, methodological applications, and contemporary relevance of Positioning Theory. Part 1 explores the movement of scholarly figures and their numerous works on the subject. It discusses the foundational origins and the historical contexts of the existing theories on positioning and new directions for scholarship. Part 2 examines the methodological and narrative investigations used for data analysis in positioning research, navigating through the epistemological orientations and theoretical landscapes of Positioning Theory. Part 3 explores numerous applications across disciplines to consider the reach and influence of positioning within and across multiple disciplines. Lastly, the authors contemplate the future directions for Positioning Theory. Featuring researchers from leading research institutions from across the globe, the book is important reading for scholars interested in positioning and Positioning Theory. We recommend this handbook for graduate-level courses in social psychology, communication, discourse studies and related disciplines.

Table of Contents

Part One: Conceptual Foundations and Explorations

01 An Introduction to Positioning Theory Past and Present Mary McVee,and Luk Van Langenhove

02 Positioning, Narrative Practices, and Positioning Theory Michael Bamberg

03 Positioning Theory, Speech Acts and Normative Orders–The Background of Ordinary Language Philosophy and Influence of Austin, Ryle and Strawson Bo Allesøe Christensen

04 Positioning and Personhood Jack Martin

05 Positioning and Goffman Cynthia Gordon

06 Positioning Theory and Dialogicality Ivana Markova

07 Pragmatism and Positioning Theory Svend Brinkman and Bo Allesøe Christensen

08 Positioning Theory and the Proposals of Foucault, Deleuze and Guattari: A Tool for Analysing Micro-Political Resistances Francisco Tirado and Ana Gálvez-Mozo

Part Two: Methods and Analytic Frameworks

09 Examining Varieties of Positioning: Considerations from the Past to the Present and into Future Pauline Harris, Rick Fisher, Thilina I. Wickramaarachchi, and Cynthia Brock

10 Positioning Theory, Narrative, and Narrative Analysis Mary McVee, Kristian Douglas, and Zhiyi Liu

11 Conversation Analysis and Positioning Theory Pasi Hirvonen

12 Positioning Theory and Interactional Ethnography: Complementary Approaches to Examining Positions and Positioning Processes W. Douglas Baker, Krisanna Machtmes, and Judith Green

13 Toward Integrative Methodological Frameworks of Positioning Theory, Social Semiotics, and Multimodality Katarina Silvestri, and Mary B. McVee

Part Three: Applications Across Disciplinary Topics

14 Positioning Theory as Design Principle to Negotiate Rights and Duties and Center Equity in Literacy Research Katherine K. Frankel, Susan S. Fields, and Ashley Houston-King

15 Positioning as Praxis, Developed in Mathematics Education Contexts Beth Herbel-Eisenmann, David Wagner, Anita Movik Simensen, Hilja Lisa Huru, and Annica Andersson

16 Positioning in Science Education Maria Varelas, Felicia Mensah, and Maria Rivera Maulucci

17 Positioning, Preschool Children, and Cultural Psychology Carolin Demuth, and Bo Allesøe Christensen

18 Positioning Theory in Online Environments Vanessa Paz Dennen

19 Using Strategic Communication Discourse Processes in Positioning Practice Melanie James, and Deborah Wise

20 How Positioning Theory and the Capability Approach to Welfare Economy Supplement One Another Steen Brock and Bo Allesøe Christensen

21 Positioning and Masculinity Nigel Edley

22 Positioning Theory in the Context of Intergroup Peace and Conflict Susilo Wibisono and Winnifred R. Louis

23 Positioning, Emotions, and Emotional Positioning Johanna Lönngren, and Maria Berge

Part Four: Future Directions and Reflections 24 Positioning Theory: Reflections and Future Directions Mary B. McVee, Bo Allesøe Christensen, Luk Van Langenhove and Cynthia Brock  

Mary B. McVee is a professor of literacy education, and director of the Center for Literacy & Reading Instruction (CLaRI) at the University at Buffalo, USA. Her research explores racialized positioning in teacher narratives. Her current research with teachers and multilingual children explores positioning and multimodal interactions in the context of engineering design. Luk Van Langenhove is Emeritus professor at the Brussels School of Governance of the Vrije Universiteit Brussel in Belgium and honorary professorial fellow at the University of Warwick, UK. He has published widely on regional integration, social sciences theory, positioning theory, and psychology. Cynthia H. Brock is a professor at the University of Wyoming where she holds the Wyoming Excellence in Higher Education Endowed Chair in Literacy Education. Brock’s scholarly research agenda centers on studying the literacy learning opportunities of elementary children from diverse backgrounds and the pre- and in-service teachers with whom they work. Bo Allesøe Christensen is an associate professor and co-director of the Center for Cultural Psychology at Aalborg University, Denmark. His research interest explores and develops the theoretical and methodological background of positioning theory within 20th century linguistic philosophy and microsociology.

Critics' Reviews

"This Handbook is a precious pearl in amidst the ever-increasing flow of empirical papers all claiming adherence to the Positioning Theory. Often these empirical studies do not go beyond locating the assumed positions in a societal or personal matrices, failing to analyze their dynamic interdependencies and transformations in time.  This Handbook stands out among the multitude of uses of the Positioning Theory in its thorough analysis of the dynamic side of the positions as these generate change in the mind and society.  The contributions in the Handbook innovate the theory and leads to new alleys for its use. The collective of authors in this Handbook is living up to their duty to revolutionize the social sciences not letting their discourses become shallow reflections of everyday language use, and they fully exercise their right for deep penetration into the intricacies of social and personal psychological phenomena in their search for general principles of psychology and sociology." Jaan Valsiner, Aalborg University, and Editor, Integrative Psychological & Behavioral Sciences

About VitalSource eBooks

VitalSource is a leading provider of eBooks.

• Access your materials anywhere, at anytime.
• Customer preferences like text size, font type, page color and more.
• Take annotations in line as you read.

Multiple eBook Copies

This eBook is already in your shopping cart. If you would like to replace it with a different purchasing option please remove the current eBook option from your cart.

Book Preview

The country you have selected will result in the following:

• Product pricing will be adjusted to match the corresponding currency.
• The title Perception will be removed from your cart because it is not available in this region.

• Latest contributions
• Volume 7 2023/24
• Volume 6, Issue 1, 2022
• Volume 5, Issue 1, September 2020
• Volume 4, Issue 1, 2019
• Volume 3, Issue 2, 2018
• Volume 3, Issue 1, 2017
• Volume 2, Issue 2, 2016
• Volume 2, Issue 1, 2016
• Volume 1, Issue 2, 2015
• Volume 1, Issue 1, 2014

• Using positioning theory in early childhood research

By Ute Ward -  Senior Lecturer, School of Education, University of Hertfordshire

In this paper, I reflect on the use of positioning theory as a theoretical framework for my doctoral thesis and for education more widely.  The paper opens with an introduction to some core concepts of positioning theory focusing on prepositioning and accountive positioning (Langenhove & Harré,1999). My doctoral research is then used to show the application of positioning theory in early childhood (EC) research. My research aimed to explore parents’ understanding of their interactions with EC practitioners and their beliefs and expectations regarding practitioner roles and responsibilities.

The research project employed a sequential mixed methods design consisting of a quantitative stage followed by a qualitative stage.  Quantitative data was gained through 97 questionnaires and led to a deeper understanding of how parents prepositioned themselves and practitioners through the allocation of rights, duties and responsibilities.  These prepositions were then explored further in interviews with 11 parents to discover how parents made sense of their prepositioning and their interactions with early childhood practitioners.

The research was carried out in accordance with BERA guidelines and received ethical approval from King’s College, London.

The findings indicated that parents understood themselves as being ultimately responsible for their children’s development and learning. Using positioning theory led to new insights into how parents enact this responsibility.  Equally parents’ narratives highlighted that practitioners were understood as resources for parents to help them meet their responsibilities.  Furthermore, parents wished to engage in a ‘caring partnership’ with practitioners.

This paper concludes with a reflection on the usefulness of positioning theory and the potential to apply it to lecturer-student relationships in the School of Education.

A brief introduction to positioning theory

I have long been interested in the relationship between EC practitioners and parents stretching back to my work in pre-schools, Sure Start local programmes and children’s centres.  It was therefore only natural to focus on this relationship for my doctoral research. My experiences as a lecturer in early childhood education enforced this choice as I am repeatedly struck by the dismissive and condescending stance some pre-service and in-service practitioners take towards parents.  In parts, this reflects government guidance and regulatory discourses which portray parents as lacking knowledge, interest or motivation and as passive in their children’s learning and development (for example, Bate, 2017).  At the same time, researchers continue to point out the ineffectiveness of practitioner-parent interactions and the discrepancy between rhetoric and reality (Hakyemez-Paul et al, 2018; Hadley, 2014; Hornby and Lafaele, 2011).   To examine causes and suggest improvements, a growing body of research now studies parents’ and practitioners’ beliefs and expectations, and their understanding of each other’s roles and responsibilities (Rogers, 2018; Hadley, 2014; Freeman et al., 2008).  One theoretical framework used in this context is role theory. Hoover-Dempsey et al explain that

“Parental role construction is defined as parents’ beliefs about what they are supposed to do in relation to their children’s education and the patterns of parental behaviour that follow those beliefs.” (Hoover-Dempsey et al, 2005, 107)

Roles are seen as sets of expectations which are influenced by societal norms.  The resulting behaviour characterises individuals or groups (Hoover-Dempsey and Sandler, 1997), and although parents’ role constructions change over time, especially as children grow older, on a day-to-day basis, roles remain stable.

Research building on role theory has made valuable contributions to understanding parents’ and practitioners’ beliefs and actions, both in schools and in EC settings (Galindo and Sheldon, 2012; Bakker and Denenssen, 2007; Hoover-Dempsey et al, 2005).  Although role theory explains how practitioner and parent encounter each other and how they behave in their relationships, it does not serve well to consider the day-to-day variations in and experiences of interactions. Lawrence-Lightfoot (2003) argues that teachers and parents approach their interactions with their histories, experiences and beliefs at the back of their minds and that teacher-parent conversations cannot be effective if we ignore what people ‘bring to the conversation’. Her views led me to explore in more detail parents’ preconceived ideas, their thought-processes and the ways in which they make sense of their own lived experience when talking to their children’s practitioners.   Role theory seemed insufficient for this, and I was struggling to find a suitable theoretical framing for my research until I encountered a small number of articles using positioning theory (Sims-Schouten, 2015; Freeman, 2010). This approach argues that variations in behaviour and misunderstandings in interactions arise from the ways in which individuals make sense of their experiences and how they rationalise their actions (Harré and Langenhove, 2010).  Positioning itself is described as

“the assignment of fluid ‘parts’ or ‘roles’ to speakers in the discursive construction of personal stories that make a person’s actions intelligible and relatively determinate as social acts.” (Harré and Langenhove, 2010, 218)

This definition locates positioning in the thinking that occurs in interactions between two people.  A position arises from the subjective history of an individual person and reflects their experiences, emotions and beliefs (Harré et al 2009; Harré and Davies, 1990). It can be described as a cluster of beliefs which expresses the normative assumptions of rights and duties that are allocated to the different participants in this interaction (Harré et al, 2009). Positioning theory is therefore well-placed to capture the nuances in interpersonal encounters and provides a theoretical framework to gain a deeper understanding of differences in people’s perspectives and beliefs.  It can reveal

“the explicit and implicit patterns of reasoning that are linked to the way that people act towards each other and how they construct themselves and their own position within this.” (Sims-Schouten, 2015, 3)

Inherent in positioning theory is the understanding that individuals are active agents in their social interactions as they can choose and shape their own positions, influence the positioning of others and co-construct positions when talking with others (Harré and Davies, 1990). This also means that individuals can reject or challenge a position that others ascribe to them (Harré and Davies, 1990).  The agentic nature of positions distinguishes them from roles which offer an expression of static social structures (Harré and Davies, 1990) and lack the dynamic nature of positions.  As agentic contributors, individuals make choices regarding the positionings that seem relevant to them in an interaction. To make sense of positions and positionings, individuals develop, either consciously or subconsciously, narratives that offer a consistent, unitary understanding of themselves (Harré and Davies, 1990).  This understanding is located in the moment; at a different time or in a different context an individual may use similar positionings but construct a different narrative (Harré and Davies, 1990).  The situatedness in time and space which builds on individual histories, beliefs and experiences contributes to positioning theory as a theoretical framework. It allows for a detailed understanding of social phenomena and lends itself to the investigation of the relationship between EC practitioners and parents.

Positioning processes

To accommodate different actions and intentions in conversations, positioning theory distinguishes a range of positioning types.  ‘Prepositioning’ highlights the attributes, character traits and assumptions about rights and duties which people hold before they enter into a dialogue (Harré et al, 2009).  Both positioning and prepositioning take place in relation to the self (self-positioning) and to others (other-positioning); they can be tacit and implied or intentional and explicit ((Harré and Langenhove, 2010). The concept of prepositioning suggests that practitioner and parent encounter each other with existing beliefs and expectations rather than with an open mind and without preconceived ideas. This aspect of positioning theory in particular facilitates the examination of ‘what parents bring to the conversation’.

In addition to positioning and prepositioning, Harré and Langenhove (2010) distinguish three different orders of positioning:

“First order positioning refers to the way persons locate themselves and others within an essentially moral space by using several categories and storylines” (Harré and Langenhove, 2010, 220).

Second order positioning occurs when a person questions how others position them and renegotiates this positioning.

Third order positioning takes place after the original encounter when a person thinks or talks about their experience and tries to make sense of it. (Langenhove and Harré, 1999)

Importantly, it is not just individuals who position themselves and others; groups, organisations and governments also position people.  Therefore, first order positioning may be evident in government documents about education or parenting, which teachers or parents may attempt to contest (second order positioning) (Langenhove and Harré, 1999). In the parent-practitioner relationship, second order positioning may occur when a parent rejects the practitioners’ attempt to position parents as passive bystanders in children’s learning and, instead, asks for greater involvement in planning for their child’s learning.

A further type of positioning is accountive positioning which refers to ‘talk about talk’ or accounting for positionings that have been experienced.   This is third order positionings as narratives are shared with others about an earlier interaction (Langenhove and Harré, 1999).  As such, accountive positioning includes an element of reflection on the original discourse which may lead to ‘repositioning’: adjusting a positioning in order to make sense of events and to (re)construct a coherent and unitary self (Harré et al, 2009).  Accountive positioning also occurs when a researcher invites interviewees to recount experiences of interactions with other people.

Researching parents’ positionings

My research project used prepositioning and accountive positioning to explore parents’ views, beliefs and attitudes and to gain an in-depth understanding of parents’ reasoning and sense-making regarding their interactions with practitioners.  I used a sequential mixed methods approach consisting of a quantitative stage followed by a qualitative stage (Creswell, 2014).  The quantitative stage used questionnaires and provided an overview of which roles and responsibilities parents allocated to themselves and to practitioners, which practitioner attributes and characteristics they valued and what type of relationship they envisaged for parents and practitioners.  The questionnaires were completed by 97 parents with children under the age of 5 years from eight EC settings in the private, voluntary and maintained sectors. The resulting data was analysed using non-parametric statistics and revealed parents’ prepositioning of themselves as competent and responsible agents in their children’s lives.  Practitioners were positioned as caring and knowledgeable professionals, and parents showed a clear preference for a partnership with practitioners. These insights were used to develop the interview schedule for the second stage which consequently explored parents’ lived experiences and their reasonings for their positionings.  The qualitative stage consisted of three paired and five individual interviews with 11 parents from three different settings.  This was a self-selected sample from the questionnaire participants. The interviews focused on accountive positioning to gain parents’ narratives and reasonings which were analysed using thematic analysis (Boyatzis, 1998).  The interviews extended the questionnaire data with greater detail on how parents enact their responsibility towards their children, on practitioners’ interactions with children and their support for parents, and on how parents describe their partnership with practitioners.

The combined analyses led to the following findings: Firstly, parents reiterated their overall responsibility for their children’s development and learning and positioned themselves as competent and confident parents.  Parents described two main ways in which they enacted their responsibility for their children in the context of early childhood settings: Initially, they carefully selected the setting and then they asked for advice from practitioners when they needed it.  The former bears some resemblance to being a customer and emphasises parents’ purchasing power but parents did not understand choosing a nursery as a commercial transaction.  Equally, changing settings mid-term was first and foremost described as taking responsibility for the child’s well-being and acting on perceived or real differences between parental expectations and setting provision.  The second way to enact their responsibility, asking for advice, may be interpreted as parents lacking knowledge which would confirm a deficit view of parents; however, parents did not focus on their perceived deficit but on their agency in addressing any lack of knowledge demonstrating their acceptance of their responsibility for their children’s development and learning.

Implicit in the way parents positioned themselves was the positioning of their children’s practitioners as a resource for parents.  Practitioners were seen as experienced professionals with expert knowledge of children and child development, and parents frequently drew on this expertise to help them in their own parenting.  This contrasts with the positioning of parents as a resource for schools and teachers in some of the parent involvement literature, for example, when parents are positioned as volunteers in the classroom or as fundraisers for the school (National College, 2011; Epstein and Sanders, 2002).

Overall, parents wanted to engage in ‘caring partnerships’ with their children’s practitioners.  Emerging from the questionnaires and repeated in the interviews was the request for caring practitioners where ‘caring’ described both the act of caring and the personal characteristic of caring.  Through the emphasis on caring this research added the parents’ voice to the findings from practitioner-based research and academic writing that described ‘caring’ as an element of early childhood professionalism (Ward, 2018; Page, 2018; Osgood, 2010).   Equally, parents asked for a partnership with practitioners which built on mutuality and collaboration to support children’s development and learning. Consequently, the findings provided some detail for the frequently used but rarely described concept of ‘partnership with parents’.

When the findings were considered alongside practitioners’ views and perceptions presented in earlier research (Ward, 2018; Osgood, 2010) a mismatch in positioning and reasoning became apparent. Where parents enacted responsibility by choosing or changing settings, practitioners perceived customer behaviour; where parents sought advice to make sound parenting decisions, practitioners saw a lack of understanding; where parents made difficult parenting decisions after consultation with experts in the setting, practitioners noticed a dismissal of their professional knowledge.  While parents and practitioners maintain contrasting positions and narratives, there is little overlap in the spheres they allocate to themselves and each other (Figure 1).  The ensuing mismatch makes it unlikely that parent and practitioner can create the mutual understanding and respect that are pre-requisites for caring partnerships.

However, the caring partnership grows when practitioner and parent position themselves and each other in similar ways and when there is considerable overlap in their respective spheres of duties, rights and responsibilities (Figure 2).  This consensus supports the development of reciprocal, respectful interactions which allow the caring partnership to flourish and grow.  This in turn will lead to consistent, harmonious care for young children in their early childhood setting and at home. (Sylva et al, 2010).

The value of positioning theory in education

The exploration of positionings in parents’ interactions with practitioners has allowed me to gain a deeper understanding of their motivations and intentions.  The finding that parents are responsible for their children is not new and can be identified from parents’ actions and behaviours.  However, the detail of how they see themselves enacting their responsibility would not have been accessible, for example, through role theory. It is the capture of preconceptions, narratives and storylines that facilitates insights into sense-making which in turn can explain subtle shifts and changes in behaviour.  Equally, both parent and practitioner may employ the storyline of the responsible parent, but there is potential for a mismatch between practitioners’ interpretation and parents’ interpretation because they allocate different positions to each other.

Harré outlines how positioning theory can be used to analyse tensions or conflict between individuals and between groups of people (Harré et al, 2009; Langenhove and Harré, 1999; Harré and Davies, 1990).  Building on his writing and the small number of research projects using positioning theory in education has enabled me to gain a deeper understanding of one aspect of parent-practitioner relationships.  This leads me to wonder whether positioning theory may also provide a tool for lecturers to reflect on interactions with students.  How do we position students?  As keen, curious, focused on academic achievement? How do they position us? As knowledgeable experts, a resource for their learning, authority figures?  When there are issues for students in placements, could these be grounded in school staff positioning students as practitioners rather than as learners? The experience with my research project leads me to suggest that we need to make our positionings more explicit and invite others to do the same.  To get things right for our students, an open approach to and respectful consideration of each other’s meanings, narratives and storylines seems to be essential.  In the School of Education (and in our University more widely), the terms ‘storyline’, ‘learner journey’ or ‘programme narrative’ have become prevalent.  These discourses seem to focus on what we are presenting to students or refer to perceived storylines.  There may be a danger that we group students together, for example, as ‘commuting students’ or as ‘BAME students’, which may reinforce prepositioning without actually entering into a dialogue with individuals to explore each other’s storylines and meaning.   I would suggest that only a closer alignment of student and tutor positionings can lead us to the collegiate learning community we want to create.

References:

Bakker, J. & Denessen, E. (2007). The concept of parent involvement. Some theoretical and empirical considerations. International Journal about Parents in Education. 1(0), 188-199.

Bate, A. (2017) Early Intervention, Briefing paper 7647, 26 June 2017. [Online] Available: https://researchbriefings.parliament.uk/ResearchBriefing/Summary/CBP-7647 [Accessed 22nd July 2018]

Boyatzis, R. (1998) Transforming Qualitative Information: Thematic analysis and code development. London: SAGE Publications Ltd.

Creswell, J. (2014) Research Design: qualitative, quantitative and mixed methods approaches, 4th edn (London: SAGE Publications).

Epstein, J. & Saunders, M. (2002) Family, School and Community Partnership. In Handbook of Parenting, Volume 5: Practical Issues in Parenting (2nd ed). Bornstein, M. (Ed) (Mahwah, New Jersey: Lawrence Erlbaum Associates).

Freeman, H., Newland, L. & Coyl, D. (2008). Father beliefs as a mediator between contextual barriers and father involvement. Early Child Development and Care. 178(7-8), 803-819, DOI: 10.1080/03004430802352228.

Freeman, M. (2010) ‘’Knowledge is acting: working class parents intentional acts of positioning within the discursive practice of involvement’. International Journal of Qualitative Studies in Education, 23 (2), 181-198, DOI: 10.1080/09518390903081629

Galindo, C. and Sheldon S. (2012) School and home connections and children’s kindergarten achievement gains, The mediating role of family involvement. Early Childhood Research Quarterly, 27, 90-103.

Hadley, F. (2014). It’s bumpy and we understood each other at the end, I hope! Unpacking what experiences are valued in the early childhood setting and how this impacts on parent partnerships with culturally and linguistically diverse families. Australasian Journal of Early Childhood. 39(2), 91-99.

Hakyemez-Paul, S., Pihlaja, P. & Silvennoinen, H. (2018). Parental involvement in Finnish day care—what do early childhood educators say? European Early Childhood Education Research Journal. 26(2), 258-273.

Harré, R., & Davies, B. (1990). Positioning: The discursive production of selves. Journal for the Theory of Social Behavior. 20, 43–63.

Harré, R., & Van Langenhove, L. (2010). Varieties of positioning. In People and societies, Van Langenhove, L. (ed) (New York, NY: Routledge).

Harré, R.; Moghaddam, F; Pilkerton Cairnie, T; Rothbart, D. & Sabat, S. (2009). Advances in Positioning Theory. Theory & Psychology. 19(1), 5-31.

Hoover-Dempsey, K, Walker, J., Sandler, H., Whetsel, D., Green, C., Wilkins, A. & Closson, K. (2005) Why do parents become involved? Research Findings and Implications. The Elementary School Journal. 106(2),105-126.

Hoover-Dempsey, K. and Sandler, H. (1997). Why do parents become involved in their children’s education? Review of Educational Research. 67(1), 3-42.

Hornby, G.& Lafaele R. (2011). Barriers to parental involvement in education: an explanatory model. Educational Review. 63(1), 37-52, DOI:10.1080/00131911.2010.488049

Langenhove, L. van, & Harré, R. (1999). Introducing positioning theory. In Positioning theory, Harré, R. and van Langenhove, L. (Ed) (Cambridge, UK: Blackwell).

Lawrence-Lightfoot, S. (2003) The Essential Conversation: What parents and teachers can learn from each other (New York: Ballantine Books).

National College for Leadership of Schools and Children’s Services (National College) (2011). Leadership for parental engagement. (Nottingham: National College).

Osgood, J. (2010). Reconstructing professionalism in ECEC: the case for the ‘critically reflective emotional professional’. Early Years. 30(2), 119-133.

Page, J. (2018). Characterising the principles of Professional Love in early childhood care and education. Early Years. 30(2), 119-133.

Rogers, S. (2018). “She thinks her toys don’t understand Romanian”: Family engagement with children’s learning during the transition to school.  European Early Childhood Education Research Journal. 26(2), 177-186.

Sims-Schouten, W. & Stittrich-Lyons, H. (2014). ‘Talking the Talk’: practical and academic self-concepts of early years practitioners in England. Journal of

Vocational Education & Training. 66(1), 39-55, DOI: 10.1080/13636820.2013.867526.

Spencer-Woodley, L. (2014). Accountability: tensions and challenges. In Early Years Policy: The impact on practice, Kingdon, Z. and Gourd, J. (ed)(Abingdon: Routledge).

Sylva, K., Melhuish, E., Sammons, P., Siraj-Blatchford, I. and Taggart, B. (2010). Early Childhood Matters Evidence from the Effective Provision of Pre-school Education Project. London: Routledge.

Ward, U. (2018). How do early childhood practitioners define professionalism in their interactions with parents? European Early Childhood Education Research Journal. 26(2), 274-284.

• Moving to Online Teaching – Concepts, Considerations and Pitfalls
• Research mentoring schemes: A personalised needs-led approach
• Online learning and teaching: reflections on the case of an online palliative day therapy programme, under COVID-19 lockdown
• An exploration of factors impacting on the ability of leaders of schools in challenging circumstances to create sustainable change

Conflict, power, and difference in dialogue: a conversation between public diplomacy and positioning theory

• Original Article
• Published: 08 May 2021
• Volume 20 , pages 44–54, ( 2024 )

Cite this article

• Andrea Pavón-Guinea 1  

342 Accesses

3 Citations

3 Altmetric

Explore all metrics

This paper explores the application of positioning theory to public diplomacy as a way to develop the theorization and empirical investigation of dialogue in the literature. First, it offers an overview of how dialogue has been conceptualized in the new public diplomacy. Secondly, it argues that there are two main problems with its current conceptualization: it is based on normative theories of communication and it does not take sufficiently into account the context where the communicative act occurs. In line with existing critical approaches to public diplomacy, the paper applies positioning theory to public diplomacy through the analysis of the case study of the Euro-Mediterranean intercultural dialogue. The preliminary conclusion is that positioning theory can enrich the theoretical foundations and empirical research of dialogue in public diplomacy and expand the use of social constructivism in IR by investigating the conditions of possibility for dialogue when relationships become mired with conflict, power, and difference.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

From Angry Monologues to Engaged Dialogue? On Self-Reflexivity, Critical Discursive Psychology and Studying Polarised Conflict

Transforming the Way We Speak, Transforming the Way We Listen: Dialogue and the Transformation of Relationships

Arsenault, A. 2009. Public diplomacy 2.0. Toward a new public diplomacy , 135–153. New York: Palgrave Macmillan.

Book   Google Scholar  

Baert, F., L. Van Langenhove, and M. James. 2019. Rethinking role theory in foreign policy analysis: Introducing positioning theory to international relations. Papers on Social Representations 28 (1): 4.1-4.20.

Google Scholar  

Baert, P. 2015. The existentialist moment: The rise of Sartre as a public intellectual . Cambridge: Polity.

Bourdieu, P. 2003. Language and symbolic power . Cambridge, MA: Harvard University Press.

Bouris, D., and T. Schumacher. 2017. The revised European neighbourhood policy: Continuity and change in EU foreign policy . London: Palgrave Macmillan.

Brockmier, J., and R. Harré. 1997. Narrative: Problems and promises of an alternative paradigm. Research on Language and Social Interaction 30 (4): 263–283.

Article   Google Scholar  

Brown, R. 2013. The politics of relational public diplomacy. Relational, networked, and collaborative approaches to public diplomacy: The connective mindshift , 56–57. London: Routledge.

Buber, M. 1958. I and Thou/with a postscript by the author added; translated by Ronald Gregor Smith . Edinburgh: T. & T. Clark.

Carbaugh, D., E.V. Nuciforo, M. Saito, and D. Shin. 2011. “Dialogue” in cross-cultural perspective: Japanese, Korean, and Russian discourses. Journal of International and Intercultural Communication 4 (2): 87–108.

Cebeci, M. (2017). The EU’s Construction of the Mediterranean. MedReset Policy Paper 1,

Comor, E., and H. Bean. 2012. America’s ‘engagement’ delusion. International Communication Gazette 74 (3): 203–220.

Council of the European Union. “Presidency Conclusions for the Euro-Mediterranean Meeting of Ministers of Foreign Affairs (The Hague 29–30 November 2004), 14869/04 (Presse 331)

Council of the European Union. “Presidency Conclusions for the Mid-Term Euro-Mediterranean Conference” (Crete 26–27 May 2003), 9890/03 (Presse 151)

Council of the European Union. “Presidency Conclusions for the Euro-Mediterranean Meeting of Ministers of Foreign Affairs (Naples 2–3 December 2003), 15380/03 (Presse 353)

Council of the European Union. “Presidency Conclusions for the Vth Euro-Mediterranean Conference of Foreign Ministers” (Valencia 22–23 April 2002), 8254/02 (Presse 112)

Council of the European Union. “Presidency Conclusions for the Euro-Mediterranean Mid-Term Meeting of Ministers of Foreign Affairs” (Dublin 5–6 May 2004), 9064/04 (Presse 137)

Cowan, G., and A. Arsenault. 2008. Moving from monologue to dialogue to collaboration: The three layers of public diplomacy. The ANNALS of the American Academy of Political and Social Science 616 (1): 10–30.

Dahlberg, L. 2013. The Habermasian public sphere and exclusion: An engagement with poststructuralist-influenced critics. Communication Theory 24 (1): 21–41.

Davies, B., and R. Harré. 1990. Positioning: the discursive production of selves. Journal for the Theory of Social Behaviour 20 (1): 43–63.

Deetz, S., and J. Simpson. 2004. Critical organizational dialogue: Open formation and the demand of “otherness.” In Dialogue: Theorizing difference in communication studies , 141–158. Thousand Oaks: Sage.

Chapter   Google Scholar  

Dolea, A. 2018. Public diplomacy as co-constructed discourses of engagement. In The handbook of communication engagement , 331–345. Hoboken: Wiley.

Dolea, A. 2015. The need for critical thinking in country promotion: Public diplomacy, nation branding and public relations. In The Routledge Handbook of critical public relations , 274–288. Hoboken: Wiley.

Dutta-Bergman, M.J. 2006. U.S. Public Diplomacy in the Middle East. Journal of Communication Inquiry 30 (2): 102–124.

European Union. 2016. Towards an EU Strategy for International Cultural Relations, Joint Communication to the European Parliament and the Council. https://ec.europa.eu/culture/policies/strategic-framework/strategy-international-cultural-relations_en

Ferri, G. 2014. Ethical communication and intercultural responsibility: A philosophical perspective. Language and Intercultural Communication 14 (1): 7–23. https://doi.org/10.1080/14708477.2013.866121 .

Fitzpatrick, K. 2013. Public diplomacy and ethics: From soft power to social conscience. In Relational, networked, and collaborative approaches to public diplomacy: The connective mindshift , 41–55. London: Routledge.

Fitzpatrick, K. R. 2011. US Public Diplomacy in a Post 9/11World: From Messaging to Mutuality. CPD Perspectives on Public Diplomacy, Paper 6

Fitzpatrick, K.R. 2010. The future of U.S. Public Diplomacy: An uncertain fate . Leiden: Brill Nijhoff.

Foucault, M. 1995. Discipline and punish: The birth of the prison . New York: Vintage Books.

Ganesh, S., and H.M. Zoller. 2012. Dialogue, activism, and democratic social change. Communication Theory 22 (1): 66–91.

Gilboa, E. 2008. Searching for a theory of public diplomacy. The ANNALS of the American Academy of Political and Social Science 616 (1): 55–77.

Gorski, P.C. 2008. Good intentions are not enough: A decolonizing intercultural education. Intercultural Education 19 (6): 515–525.

Graham, S.E. 2014. Emotion and public diplomacy: Dispositions in international communications, dialogue, and persuasion. International Studies Review 16 (4): 522–539.

Gregory, B. 2008. Public diplomacy: Sunrise of an academic field. The ANNALS of the American Academy of Political and Social Science 616 (1): 274–290.

Habermas, J. 1986. The theory of communicative action . Cambridge: Polity.

Handelman, D. 2008. Afterword: Returning to cosmology—Thoughts on the positioning of belief. Social Analysis 52 (1): 181–195.

Harré, R. 2012. Positioning theory: Moral dimensions of social-cultural psychology. Oxford Handbooks Online . https://doi.org/10.1093/oxfordhb/9780195396430.013.0010 .

Harré, R., F.M. Moghaddam, T.P. Cairnie, D. Rothbart, and S.R. Sabat. 2009. Recent advances in positioning theory. Theory & Psychology 19 (1): 5–31.

Harré, R., and F.M. Moghaddam. 2003. The self and others: Positioning individuals and groups in personal, political, and cultural contexts . Westport: Praeger.

Harré, R., and N. Slocum. 2003. Disputes as complex social events: On the uses of positioning theory. In The self and others: Positioning individuals and groups in personal , 123–136. West Port: Political and Cultural Contexts. Greenwood Publishing Group.

Harré, R., and L. Van Langenhove. 1991. Varieties of positioning. Journal for the Theory of Social Behaviour 21 (4): 393–407.

Harrison, T.R., and J.W. Muhamad. 2018. Engagement in conflict. In The handbook of communication engagement , 187–204. Hoboken: Wiley.

Hermans, H., and A. Hermans-Konopka. 2010. Dialogical self theory positioning and counter-positioning in a globalizing society . Cambridge: Cambridge University Press.

Hollway, W. 1984. Gender differences and the production of subjectivity. In Changing the subject: Psychology, social regulation and subjectivity , 227–263. Milton Park: Taylor & Francis Group.

James, M. 2014. Positioning theory and strategic communications: A new approach to public relations research and practice . Abingdon: Routledge.

James, M. 2010. The Use of Intentional Positioning Techniques in Government Agencies’ Communication Campaigns, Government Communication: Proceedings of the 17 th International Public Relations Research Symposium BledCom , pp. 140–137

Kennedy, A.K., and E.J. Sommerfeldt. 2018. Habits of the heart and mind. In The Handbook of Communication Engagement , 357–370. Hoboken: Wiley.

Louis, W.R. 2008. Intergroup positioning and power. In Global conflict resolution through positioning analysis , 21–39. New York: Springer.

Macdonald, M.N., P. Holmes, and V. Crosbie. 2014. Editorial. Language and Intercultural Communication 14 (2): 151–155.

Maclennan, J. 2011. “To build a beautiful dialogue”: Capoeira as contradiction. Journal of International and Intercultural Communication 4 (2): 146–162.

Melissen, J. 2005. Wielding soft power: The new public diplomacy . The Hague: Netherlands Institute of International Relations “Clingendael.”

Miller, D. 2013. The morality play: Getting to the heart of media influence on foreign policy. In: Foreign correspondence . London: Routledge.

Moghaddam, F.M., and R. Harré. 2010. Words of conflict, words of war: How the language we use in political processes sparks fighting . Santa Barbara, CA: Praeger.

Moghaddam, F.M., R. Harré, and N. Lee. 2008. Global conflict resolution through positioning analysis . New York: Springer.

Moghaddam, F.M., and K.A. Kavulich. 2008. Nuclear positioning and supererogatory duties: The illustrative case of positioning by Iran, the United States and the European Union. In Global conflict resolution through positioning analysi , 247–260. New York: Springer.

Mor, B.D. 2007. The rhetoric of public diplomacy and propaganda wars: A view from self-presentation theory. European Journal of Political Research 46 (5): 661–683.

O’Loughlin, B. 2013. Book review: New public diplomacy in the 21st century: A comparative study of policy and practice, New public diplomacy in the 21st century: A comparative study of policy and practice. Media, War & Conflict 6 (3): 330–332.

Pacher, A. 2018. Strategic publics in public diplomacy: A typology and a heuristic device for multiple publics. The Hague Journal of Diplomacy 13 (3): 272–296.

Pamment, J. 2013. New public diplomacy in the 21 century: A comparative study of policy and practice . London: Routledge.

Phipps, A. 2014. ‘They are bombing now’: ‘Intercultural Dialogue’ in times of conflict. Language and Intercultural Communication 14 (1): 108–124.

Article   MathSciNet   Google Scholar  

Riis, H.B. 2017. It doesn’t matter if you’re Black or White: Negotiating identity and danishness in intercultural dialogue meetings. Journal of Intercultural Studies 38 (6): 694–707.

Riitaoja, A., and F. Dervin. 2014. Interreligious dialogue in schools: Beyond asymmetry and categorisation? Language and Intercultural Communication 14 (1): 76–90.

Riordan, S. 2005. Dialogue-based public diplomacy: A new foreign policy paradigm? In The new public diplomacy , 180–195. New York: Springer.

Said, E.W. 2003. Orientalism . New York: Vintage Books.

Saunders, H.H. 2013. The relational paradigm and sustained dialogue. In Relational, networked, and collaborative approaches to public diplomacy: The connective mindshift , 140–151. London: Routledge.

Schmidle, R. 2008. Positioning and military leadership. In Global conflict resolution through positioning analysis , 189–206. New York: Springer.

Scott-Smith, G. 2008. Mapping the undefinable: Some thoughts on the relevance of exchange programs within international relations theory. The ANNALS of the American Academy of Political and Social Science 616 (1): 173–195.

Sevin, E. 2015. Pathways of connection: An analytical approach to the impacts of public diplomacy. Public Relations Review 41 (4): 562–568.

Slocum-Bradley, N. 2008. Discursive production of conflict in Rwanda. In Global conflict resolution through positioning analysis , 207–226. New York: Springer.

Theunissen, P. 2018. Philosophy and ethics of engagement. In The handbook of communication engagement , 49–60. Hoboken: Wiley.

Trobbiani, R. 2017. EU cultural diplomacy in the MENA region: A qualitative mapping of initiatives promoting regional cooperation, Working Paper, EL-CSID, issue 2017/2 , pp. 1–47

Van Ham, P. 2008. Place branding: The state of the art. The ANNALS of the American Academy of Political and Social Science 616 (1): 126–149.

Van Ham, P. 2002. Branding territory: Inside the wonderful worlds of PR and IR theory. Millennium: Journal of International Studies 31 (2): 249–269.

Van Langenhove, L. 2017. Varieties of moral orders and the dual structure of society: A perspective from positioning theory. Frontiers in Sociology 2: 9.

Van Langenhove, L. 2011. People and societies . London: Routledge.

Van Langenhove, H. 1999. Positioning theory: Moral contexts of international action . Oxford: Blackwell.

Van Langenhove, L., and R. Harré. 1994. Cultural stereotypes and positioning theory. Journal for the Theory of Social Behaviour 24 (4): 359–372.

Vanc, A.M., and K.R. Fitzpatrick. 2016. Scope and status of public diplomacy research by public relations scholars, 1990–2014. Public Relations Review 42 (3): 432–440.

Weizman, E. 2008. Positioning in media dialogue: Negotiating roles in the news interview . Amsterdam: Benjamins.

Wise, D., and M. James. 2013. Positioning a price on carbon: Applying a proposed hybrid method of positioning discourse analysis for public relations. Public Relations Inquiry 2 (3): 327–352.

Witteborn, S. 2011. Discursive grouping in a virtual forum: Dialogue, difference, and the “intercultural.” Journal of International and Intercultural Communication 4 (2): 109–126.

Zaharna, R.S. 2018. Culture and communication insights from public diplomacy. In The handbook of communication engagement , 313–330. Hoboken: Wiley.

Zaharna, R.S. 2014. Battles to bridges: Us strategic communication and public diplomacy after 9/11 . Basingstoke: Palgrave Macmillan.

Zaharna, R.S., A. Arsenault, and A. Fisher. 2013. Relational, networked, and collaborative approaches to public diplomacy: The connective mindshift . London: Routledge.

Zaharna, R.S. 2010. Battles to bridges: U.S. strategic communication and public diplomacy after 9/11 . Basingstoke: Palgrave Macmillan.

Download references

Author information

Authors and affiliations.

Public Communication Department, School of Communication, University of Navarra, 27 González Besada, 33007, Oviedo, Asturias, Spain

Andrea Pavón-Guinea

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Andrea Pavón-Guinea .

Ethics declarations

Conflict of interest.

The corresponding author states that there is no conflict of interest.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Pavón-Guinea, A. Conflict, power, and difference in dialogue: a conversation between public diplomacy and positioning theory. Place Brand Public Dipl 20 , 44–54 (2024). https://doi.org/10.1057/s41254-021-00207-5

Download citation

Revised : 15 August 2020

Accepted : 01 April 2021

Published : 08 May 2021

Issue Date : March 2024

DOI : https://doi.org/10.1057/s41254-021-00207-5

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Public diplomacy
• Positioning theory
• International relations
• Social constructivism
• Find a journal
• Publish with us
• Track your research

Article  

• Volume 28, issue 16
• HESS, 28, 3717–3737, 2024
• Peer review
• Related articles

Estimating velocity distribution and flood discharge at river bridges using entropy theory – insights from computational fluid dynamics flow fields

Farhad bahmanpouri, tommaso lazzarin, silvia barbetta, tommaso moramarco, daniele p. viero.

Estimating the flow velocity and discharge in rivers is of particular interest for monitoring, modeling, and research purposes. Instruments for measuring water level and surface velocity are generally mounted on bridge decks, and this poses a challenge because the bridge structure, with piers and abutments, can perturb the flow field. The current research aims to investigate the applicability of entropy theory to estimate the velocity distribution and the discharge in the vicinity of river bridges. For this purpose, a computational fluid dynamics (CFD) model is used to obtain three-dimensional flow fields along a stretch of the Paglia River (central Italy), where a historical multi-arch bridge strongly affects flood flows. The input data for the entropy model include the cross-sectional bathymetry and the surface velocity provided by the numerical simulations. A total of 12 samples, including three different flow conditions at four cross-sections, one upstream and three downstream of the bridge, are considered. It is found that the entropy model can be reliably applied upstream of the bridge, also when forced with a single (i.e., the maximum) value of the surface velocity, with errors on total discharge below 13 % in the considered case. By contrast, downstream of the bridge, the wakes generated by the bridge piers strongly affect the velocity distribution, both in the spanwise and in the vertical directions and for very long distances. Here, notwithstanding the complex and multimodal spanwise distribution of flow velocity, the entropy model estimates the discharge with error lower than 8 % if forced with the river-wide distribution of the surface velocity. The present study has important implications for the optimal positioning of sensors and suggests the potential of using CFD modeling and entropy theory jointly to foster greater knowledge of river systems.

• Article (PDF, 12403 KB)
• Supplement (3532 KB)
• Article (12403 KB)
• Full-text XML

Bahmanpouri, F., Lazzarin, T., Barbetta, S., Moramarco, T., and Viero, D. P.: Estimating velocity distribution and flood discharge at river bridges using entropy theory – insights from computational fluid dynamics flow fields, Hydrol. Earth Syst. Sci., 28, 3717–3737, https://doi.org/10.5194/hess-28-3717-2024, 2024.

Velocity and discharge measurements in rivers are fundamental for monitoring, modeling, and research purposes (Depetris, 2021; Di Baldassarre and Montanari, 2009; Dottori et al., 2013; Gore and Banning, 2017; Herschy, 2009). Unfortunately, measuring river discharge can be very challenging for different reasons, for example in the case of intermittent rivers typical of semi-arid regions, of flash floods in mountain areas, of flood flows involving wide floodplains, and of freshwater flows affected by saline tidal intrusions in estuaries. While monitoring river discharge on the ground has definite advantages (Fekete et al., 2012), the use of traditional methods such as current meters and acoustic Doppler current profilers (ADCPs) is generally expensive, time-consuming, and risky for operators, particularly during severe flow conditions, and such methods are not applicable in remote and inaccessible locations. Different techniques can be used to measure the surface velocity, also during severe flood conditions, including large-scale particle image velocimetry (LSPIV) (Eltner et al., 2020; Jodeau et al., 2008; Le Coz et al., 2010; Muste et al., 2011, 2014), space–time image velocimetry (STIV) (Fujita et al., 2007, 2019), infrared quantitative image velocimetry (Schweitzer and Cowen, 2021), and other methods based on the use of either terrestrial or autonomous aerial system sensors (Bandini et al., 2020, 2021; Herschy, 2009). Indirect methods have been proposed to estimate the flow discharge using these kinds of remotely sensed data (Bogning et al., 2018; Fekete and Vörösmarty, 2002; Spada et al., 2017; Vandaele et al., 2023; Zhang et al., 2019). The flow rate is generally obtained by applying suitable velocity coefficients to estimate the depth-averaged velocity or by integrating a hypothetical flow velocity distribution in the cross-sectional area. The key point is thus estimating the depth-averaged velocity, or its full cross-sectional distribution, starting from surface velocity data, a process whose reliability depends on the (un)evenness of the actual velocity distribution.

In natural rivers with large cross-sections, the streamwise velocity typically shows a logarithmic vertical distribution, mainly determined by the bottom roughness. According to field data, the maximum velocity is found just below the free surface and gradually decreases towards the bed (Franca et al., 2008; Guo, 2014). However, plenty of factors contribute to making the velocity distribution irregular. For instance, channel bends and deformed bathymetry produce large-scale secondary currents (Constantinescu et al., 2011; Lazzarin and Viero, 2023; Yang et al., 2012), and the presence of banks and of discontinuities of bed elevation in the spanwise directions can generate secondary currents of the second kind because of turbulence heterogeneity (Nikora and Roy, 2011; Proust and Nikora, 2020), which all increase the three-dimensionality of the flow field and alter the vertical and spanwise distributions of the flow velocity.

The presence of in-stream structures, such as bridges characterized by the presence of piers and/or of lateral abutments, can induce sudden variations of the flow field (Laursen, 1960, 1963) and complex three-dimensional turbulent structures (Ataie-Ashtiani and Aslani-Kordkandi, 2012; Chang et al., 2013; Lazzarin et al., 2024a; Salaheldin et al., 2004). Secondary currents in the cross-section transport low momentum fluid from lateral regions to the center of the channel and high-momentum fluid from the free surface toward the bed (Bonakdari et al., 2008; Nezu and Nakagawa, 1993; Yang et al., 2004). Coherent systems of vortices with horizontal (horseshoe vortex) or vertical axes (wake vortex) modify the velocity distribution (Kirkil and Constantinescu, 2015; Sumer et al., 1997). The wakes generated by in-stream obstacles and contractions can produce uneven spatial distributions of the water surface elevations close to the bridge and can propagate downstream of bridges, thus altering the cross-sectional velocity distribution for quite long distances (Briaud et al., 2009; Yang et al., 2021). Furthermore, because of particular bridge shape (e.g., arch-piers) and irregular cross-sections (e.g., compound sections), the flow field may show a marked dependence on the water depth and the flow rate.

Even though the above factors complicate estimation of the cross-sectional velocity distribution (and thus the flow discharge) based on surface velocity data in the vicinity of in-stream structures, it has to be observed that measuring instruments such as hydrometers, as well as radar sensors or cameras for estimating the surface velocity, are often mounted on bridge decks for convenience reasons. Notwithstanding the recommendation of installing height gauge at the upstream side of bridges (Meals and Dressing, 2008), measuring instruments are often located downstream of bridges, where the flow field unevenness is expected to further complicate the discharge estimation (Kästner et al., 2018). Besides the measurement of the flow discharge, knowing the flow field nearby bridges has additional practical implications; the flow velocity is the dominant parameter to study the local scour at bridge piers, which may cause bridge collapse during floods (Barbetta et al., 2017; Cheng et al., 2018; Federico et al., 2003; Khosronejad et al., 2012; Lu et al., 2022).

One of the most promising methods to estimate the cross-sectional velocity distribution from joint measures of water level and surface velocity is based on the concept of entropy. Researchers have widely applied this concept to predict the velocity distribution, flow discharge, and other relevant parameters of open-channel flows (Bahmanpouri et al., 2022b; Bonakdari et al., 2015; Chahrour et al., 2021; Chiu, 1989; Chiu et al., 2005; Chiu and Said, 1995; Ebtehaj et al., 2018; Moramarco et al., 2019; Moramarco and Singh, 2010; Singh et al., 2017; Sterling and Knight, 2002; Termini and Moramarco, 2017; Vyas et al., 2021). Recent applications of the entropic velocity distribution include the case of large meandering channels (Termini and Moramarco, 2020), the estimation of the depth-averaged velocity as a function of the aspect ratio (Abdolvandi et al., 2021), the confluence of the large Negro and Solimões rivers (Bahmanpouri et al. 2022a), and the regionalization of the entropy parameter (Ammari et al., 2022). One advantage of the entropy approach is providing the complete cross-sectional distribution of velocity, whereas other indirect methods for estimating flow discharge only compute the depth-averaged value from the surface velocities at subsections using a fixed reduction coefficient (e.g., Le Coz et al., 2010). Previous studies demonstrated the accuracy of the entropy method in undisturbed flow conditions and also in cases like confluences or low-curvature bends characterized by large-scale three-dimensional effects and secondary currents.

The present research is meant to investigate the predictive ability of entropy theory in estimating the velocity distribution, and hence the streamflow discharge, in the case of complex flow fields generated by the presence of bridges. The issue is of particular relevance because, as already noted, water levels and free-surface velocities are often measured by instruments mounted on bridges, where the flow–structure interaction can significantly disturb the flow field.

Considering that measuring the cross-sectional velocity distribution in the vicinity of bridges is practically unfeasible in flood conditions, in the present study a three-dimensional computational fluid dynamics (3D-CFD) model is used to obtain physics-based and high-resolution descriptions of the real flow field, for a sufficiently long river segment and for different values of the flow discharge. The CFD-computed surface velocity (either a single value or its river-wide distribution) is used as input for the entropy model, thus simulating the availability of suitable data provided by remote sense instruments. Then, the cross-sectional velocity distributions provided by the entropic model are benchmarked against those computed by the CFD model, which allows the reliability of the entropy model to be assessed. The exercise is repeated for different cross-sections, both upstream and downstream of the bridge, to investigate the pros and cons of different locations where estimating the discharge and thus to provide applicative guidelines. A reach of the Paglia River, in central Italy, is chosen as a relevant case study; here, a level gauge and a radar sensor for measuring the surface velocity are mounted on a historical multi-arch bridge, which produces strong flow–structure interactions.

The present analysis allows guidelines to be provided for the proper application of entropy theory and the optimal choice and positioning of measuring instruments, aimed at the reliable estimation of flow discharge in the vicinity of river bridges.

2.1  Field site

The Paglia River, in the central part of Italy (Fig. 1a), is a tributary of Tiber River, subject to severe flooding and high sediment transport. The reach of interest, near the town of Orvieto, is across the Adunata bridge (Fig. 1b) along the Paglia River (basin area of about 1200 km 2 , average discharge of 10 m 3  s −1 , flood discharge up to 2500 m 3  s −1 ). The Adunata bridge connects the settlements of Orvieto Scalo and Ciconia, as part of the Italian State Road no. 71 (Fig. 1c). It is a masonry multi-arch bridge, with five arches ending at four piers on the river bed. On the right-hand side, an abutment sustains the bridge and separates it from the floodplain; on the left-hand side, the bridge deck is supported by the main levee. Close to the bottom, the piers have a roughly elliptical shape with the major axis, aligned with the flow, 15 m long, and the minor axis, orthogonal to the flow, 5.7 m wide. At the bottom, each pier is sustained by an elliptical plinth, whose profile is 2.0 m larger than the pier. The center distance between the piers is 23.2 m. The pier width increases approaching the deck because of the arches; the deck width is approximatively 10 m.

Figure 1 (a)  Location of the field site; (b)  downstream view of the Adunata bridge on the Paglia River during normal flow condition (11 November 2021); (c)  digital terrain model (DTM) nearby the Adunata bridge (dotted line), with the domain of the 3D CFD model (black line); and (d)  location of the level gauge and of the radar sensor with the field of view (FOV) in an aerial image (© Google Earth, 2023).

The main thread of the flow is on the right-hand side of the river, and a large depositional area forms on the left-hand side just downstream of the bridge (Fig. 1b). The main channel axis is characterized by a significant curvature, bending to the left at the bridge section (Fig. 1c).

2.2  Available data

At the downstream side of the Adunata bridge, a water level gauge and a radar sensor for measuring the water surface velocity are located at the center of the first and second arch, respectively (Fig. 1d). The time resolution of both the sensors is 10 min. In addition, a number of flow rate measures and cross-sectional velocity distributions were provided by the Umbria Region Hydrological Service. The flow rate data were collected using a current meter by wading a few tens of meters downstream of the Adunata bridge in the period 2009–2011 (flow rate ranging between 3.3 and 14.3 m 3  s −1 ), and from the bridge in the period 1995–2010 (flow rate ranging between 16.8 and 147 m 3  s −1 ); additional flow rate data were collected using an acoustic Doppler current profiler (ADCP) some hundreds of meters upstream of the bridge in the period 2014–2019 (flow rate ranging between 0.37 and 45 m 3  s −1 ). The official rating curve for the Adunata bridge, provided by ARPA Lazio, is based on these measurements.

As detailed in the following sections, the rating curve derived from current meter and ADCP data, the water levels, and the free-surface velocity data collected by the sensors mounted on the Adunata bridge were used to validate the hydrodynamic numerical models (Sect. 2.3 and Appendix A). The cross-sectional velocity distributions measured with the current meter just downstream of the bridge were used to further assess the spatial variability of the entropy-based velocity distributions, as detailed in Sect. 3.1.

2.3  Numerical model

The commercial CFD software STAR-CCM + (Siemens) was used for the numerical simulations. It implements the finite-volume method to compute the flow field on unstructured, Cartesian computational grids. The software has been used and validated in several applications, including complex flows over deformed bathymetry, in the presence of obstacles (Chang et al., 2013; Kirkil et al., 2009; Lazzarin et al., 2023c, 2024b) and channel bends (Constantinescu et al., 2011, 2013; Koken et al., 2013). In the present application, the two-phase volume-of-fluid (VoF; Hirt and Nichols, 1981) method was used to track the water–air interface within the computational domain (Horna-Munoz and Constantinescu, 2018; Lazzarin et al., 2023b; Li and Zhang, 2022; Luo et al., 2018; Yoshimura and Fujita, 2020). STAR-CCM + was used to solve the Reynolds-averaged Navier–Stokes (RANS) equations, in which the stress tensor in the momentum equations is related to the mean flow quantities by adopting the Boussinesq approximation. The eddy viscosity,  μ T , was determined by solving transport equations for the turbulent kinetic energy,  k , and dissipation rate,  ε , according to the realizable k – ε turbulence model (Shih et al., 1995), suitable for large-scale complex flows in natural rivers (e.g., Horna-Munoz and Constantinescu, 2018).

The computational domain reproduced a ∼1100  m long reach of the Paglia River (Fig. 1c), centered at the Adunata bridge. The average size of the grid elements was 1.0 m. Starting 100 m upstream of the bridge and up to 300 m downstream of the bridge, the grid was refined using elements with average length of 0.5 m. To capture the near-wall boundary layer well, a prism layer refinement with three layers was used to reduce the wall-normal thickness of the grid cells close to solid boundaries (i.e., the riverbed and bridge structure). The final computational grid was made of ∼4  million elements. A rough-wall, no-slip condition was imposed at the solid boundaries by means of a wall function (roughness height of 0.1 m at the bottom, and of 0.01 m at the bridge surfaces). The upper boundary of the computational grid was treated as a symmetry plane (i.e., slip condition) for the airflow. The water elevation at the outlet (i.e., downstream section) was kept fixed in time by imposing a suitable hydrostatic-pressure distribution. The value of the downstream level, for each of the simulated scenarios, was derived from an auxiliary two-dimensional (2D), depth-averaged hydrodynamic model calibrated on available data; the 2DEF model has been used for this purpose (see Appendix A for details on the model and its calibration/verification). A constant-in-time, logarithmic velocity distribution was imposed as the upstream boundary condition for the water fraction. For the air fraction (upper part of the numerical domain), zero velocity and zero pressure were imposed at the inlet and at the outlet, respectively. The simulations were advanced in time with an implicit, first-order discretization, until steady-state conditions were reached.

The 3D-CFD model was validated by comparing the surface velocity computed by the model with that measured by the radar sensor located downstream of the bridge (see the yellow bullets in Fig. A2c and d).

2.4  Flood events considered in the study

Three different steady flow conditions have been simulated with the 3D-CFD model STAR-CCM + , which correspond to the peak flow conditions of flood events that occurred in 2012, 2019, and 2022, as provided by the rating curve for the Adunata bridge (Table 1). In all three of the flow conditions, water flowed in the main channel and over the sediment bars that are dry in the low-flow condition of Fig. 1b and d. During the most severe flood of 2012, water also flowed on the floodplains adjacent to the main river and caused the incipient pressurization of flow below the bridge arches. The preliminary simulation carried out with the 2DEF depth-averaged model showed that, at the peak of the 2012 flood event, 700 m 3  s −1 flowed through the floodplain, overflowing the bridge access roads, and 1800 m 3  s −1 flowed within the main channel; this last value was used in the 3D-CFD simulation, which considered only the main channel of the river. The flood events of 2019 and 2022, although being quite ordinary, were the largest floods that occurred after the installation of the radar sensor for the surface velocity (thus, surface velocity data were not available for the 2012 flood).

Table 1 Simulations performed in the present work. The value in brackets indicates the total discharge with consideration of the flow over floodplains, which is not considered in the 3D simulations.

Download Print Version | Download XLSX

2.5  Entropy theory

Entropy theory deals with physical systems that may have a large number of states from a probabilistic point of view. The concept of entropy is used for statistical inference, to determine a probability distribution function when the available information is limited to some average quantities, defined as constraints such as mean and variance. For the application of entropy to streamflow measurements, the pioneer was Chiu (1987), who developed a probabilistic formulation of the cross-sectional velocity distribution in open channels, in which the expected value of the point velocity is determined by applying the maximum entropy principle (Chiu, 1987, 1988, 1989). Using this probabilistic formulation, the velocity distribution is given analytically as a function of the cross-sectional geometry; of the dimensionless entropy parameter,  M ; and possibly of the depth at which the maximum velocity occurs (the so-called dip,  h ). There is a one-to-one correspondence between  M and the ratio of mean to maximum velocity in the cross-section, which is defined as the entropic function,  ϕ ( M ) (Chiu, 1991). In general, for a given river site, the magnitude of  M and, in turn, of  ϕ ( M ) , mainly depends on hydraulic parameters such as roughness and hydraulic radius, whereas they are poorly affected by the flow discharge (Chiu and Murray, 1992; Moramarco and Singh, 2010). Moreover, ϕ ( M )  is consistently found to be nearly constant at different cross-sections through gauged river sites for different flow conditions (Moramarco and Singh, 2010; Ammari et al., 2022). This is because the value of ϕ ( M ) is associated with geometric and hydraulic characteristics that tend to vary smoothly within a river system (Ammari et al., 2022).

The estimation of cross-sectional velocity distribution,  U ( x , y ) , developed by Chiu (1989), was later simplified by Moramarco et al. (2004). Using this approach, one can divide the wet cross-sectional area into N v  verticals and determine the entropy-based velocity profile along each vertical as

where U  is the time-averaged velocity, U max ( x i )  is the maximum value of  U along the i th vertical, x i  is the distance of the i th sampled vertical from the left bank, h ( x i )  is the dip (i.e., the depth of  U max ( x i ) below the water surface), D ( x i )  the flow depth, and y  is the vertical distance from the bed. The relationship between the entropic parameter,  M , and the entropic function,  ϕ ( M ) , is (Chiu, 1989)

in which U m  and U MAX  are the average and maximum flow velocities within the entire cross-section. It is worth mentioning that U m  represents the expected value of velocity that can be different from the observed mean velocity (Marini and Fontana, 2020). These two values are quite similar in the case of wide rivers (aspect ratio larger than 5). In the present research, considering the large aspect ratio for all cross-sections (Table 2), this hypothesis is valid.

Table 2 Flow data for the cross-sections of Fig. 2 and the three considered flood events of Table 1. The values of the entropic function,  ϕ ( M ) , and parameter,  M , are obtained from the 3D-CFD velocity distributions and estimated according to Eq. (4).

Introducing the variable δ ( x i ) = D t ( x i ) / [ D ( x i ) - h ( x i ) ] , the velocity dip,  h ( x i ) , is estimated according to Yang et al. (2004) from the spanwise distribution of  δ ( x i ) , which is given as

in which x min  is the spanwise distance of the x i  vertical from the nearest bank. Note that h ( x i )=0 and δ ( x i )=1 when the maximum velocity occurs at the free surface.

In the case of gauged cross-sections,  ϕ ( M ) can be inferred from measured mean and maximum flow velocities (e.g., with ADCP). For ungauged sites,  ϕ ( M ) can be estimated as (Moramarco and Singh, 2010)

where y 0  is the vertical coordinate, taken from the bottom, where the velocity is zero; k  is the von Karman constant; R  is the hydraulic radius; n  is the Manning roughness; D  is the maximum water depth; and h  is computed with Eq. (3) at the thalweg, i.e., where the water depth is maximum. According to van Rijn (1982), y 0 =0.065 ξ d 90 , where d 90  is the 90th percentile for grain size and ξ  a parameter ranging from 1 to 10 (Ferro, 2003; Moramarco and Singh, 2010).

When only the surface velocities,  U surf ( x i ) , are available at a river site, then U m a x ( x i ) can be estimated as (Fulton and Ostrowski, 2008)

For the current research, the methodological steps to estimate the cross-sectional velocity distribution (and hence the flow discharge) using entropy theory are as follows. The input data are the river-wide velocity distribution at the free-surface,  U surf , provided by the 3D-CFD model. When only the maximum value of  U surf is used as input, corresponding to the hypothetical case in which only point-sensor data are available, the spanwise distribution of  U surf is obtained by applying either a parabolic or an elliptical spanwise distribution (Bahmanpouri et al., 2022a). The velocity dip is computed using Eq. (3). The cross-sectional velocity distribution is then obtained using an iterative procedure, in which p  denotes the iteration. At the first iteration, the entropic function, ϕ ( M ) p =1 , is computed with Eq. (4), and M p =1 is computed with Eq. (2). After computing the maximum velocity for each vertical, U max ( x i ) p =1 , with Eq. (5), Eq. (1) allows the entropic velocity distribution in the whole cross-section, U ( x i , y ) p = 1 , to be estimated. The following iteration starts by computing the average and the maximum flow velocities,  U m and  U MAX , from the velocity distribution obtained in the previous iteration and then ϕ ( M ) p = U m / U MAX , M p  using Eq. (2), U max ( x i ) p with Eq. (5), and the velocity distribution U ( x i , y ) p with Eq. (1). The iterative procedure continues until the difference ϕ ( M ) p – ϕ ( M ) p −1 becomes lower than 0.01. For more details, the reader is referred to Moramarco et al. (2017).

The comparison between the entropy-based and the CFD-derived velocity distributions was performed considering four cross-sections (Fig. 2), at a distance of 50 m upstream and 50, 100, and 200 m downstream of the bridge, and the three flood events of 2012, 2019, and 2022 (see Table 1). The sections just upstream and downstream of the bridge are located at a distance of about 0.45  B from the bridge, with B ∼110  m the width of the river at the bridge section. This is a short distance, relevant for the application given that the remote sensors for surface velocity (such as radar and large-scale particle image velocimetry (PIV)) have their field of view located some tens of meter upstream or downstream of the bridge. The sections far downstream are considered to assess how far the flow field is affected by the presence of the bridge.

Figure 2 Location of the Adunata bridge and of the four selected cross-sections (aerial image from © Google Earth 2023).

First, the study analyzed the variability of the entropy function,  ϕ ( M ) , at the four cross-sections, as derived from the cross-sectional velocity distributions provided by both the 3D-CFD model and the current meter measures (Sect. 3.1). Then, in applying the entropy model to estimate the cross-sectional velocity, two different procedures were considered. In the first one, the entropy model was forced with the river-wide distribution of the surface velocities computed by the 3D-CFD model (this is described in the following Sect. 3.2); in the second one, only the maximum value of the surface velocity computed by the 3D-CFD model was considered to be input for the entropy model (Sect. 3.3). The first procedure was applied to all the four cross-sections, whereas the latter was only applied to cross-sections 1 and 4, i.e., where the effects of the bridge piers are minimal and thus the spanwise velocity distribution is unimodal.

3.1  Variability of the entropy function

Some relevant parameters that characterize the flow field (e.g., aspect ratio, average and maximum velocity) at the selected cross-sections are presented in Table 2 for the peak flow condition of the three flood events. The values of the entropic function,  ϕ ( M ) CFD , were first computed as the ratio of average to maximum velocity within the cross-section provided by the 3D-CFD model. Then, assuming the site as being ungauged,  ϕ ( M ) Eq. (4) was estimated using Eq. (4) with d 90 =0.01  m (Pilbala et al., 2024) and a Manning parameter,  n , equal to 0.035 m - 1 / 3 s at the upstream ( −50  m) and far downstream sections ( +100  and +200  m) and equal to 0.055 m - 1 / 3 s just downstream of the bridge ( +50  m cross-section), where larger energy losses are expected because of the wakes generated by the bridge piers. The values of  ϕ ( M ) Eq. (4) , reported in Table 2 and corresponding with the points marked with dashed lines in Fig. 3b, were obtained using ξ =5 to compute  y 0 (Sect. 2.5 just after Eq. 4), and the gray band was obtained by varying  ξ in the range [1, 10]. Finally, the values of the entropic parameter associated with the different values of  ϕ ( M ) are computed using Eq. (2).

Figure 3 Entropic function  ϕ ( M ) , for the different simulated scenarios, as a function of the distance from the bridge (positive downstream), (a)  computed from the 3D-CFD flow fields and (b)  estimated with Eq. (4), where the lines refer to the average values, and the gray band is obtained by varying the reference height  y 0 in Eq. (4) within the expected range. Green circles refer to data derived from velocity distributions measured with the current meter just downstream of the bridge.

Since the entropic function is typically assumed to be constant for all flow conditions at a given cross-section, it is of interest to analyze its actual variation by exploiting the flow fields provided by the 3D-CFD model and to see the effectiveness of their first-guess estimates obtained using Eq. (4). The values of  ϕ ( M ) reported in Table 2 are plotted in Fig. 3 as a function of the downstream distance from the bridge. At the first cross-section downstream of the bridge (i.e., cross-section 2), although referring to different flow conditions, the values of the entropic function computed with the 3D-CFD and the current meter velocity distributions show the same magnitude, further confirming the reliability of the 3D-CFD model. The first-guess estimates of  ϕ ( M ) in Fig. 3b, although they have a marginal role on the entropy-based computations, show a similar trend to the 3D-CFD estimates (Fig. 3b), provided that the increased Manning parameter is used at the section just downstream of the bridge. The need to calibrate such an increased Manning parameter complicates efforts in the case of disturbed flows.

Figure 4 Flood event of 2019, cross-section 2 (50 m downstream of the bridge). Velocity distributions provided by (a)  the 3D-CFD model and (b)  the entropy model forced with the river-wide distribution of the free-surface velocity. Comparison of vertical distributions of velocity at 0.2  B   (c) , 0.5  B   (d) , and 0.8  B   (e) , where B  is the width of the cross-section.

For each flood event, at cross-sections 1 and 4, i.e., where the flow field is not characterized by the wakes generated by the bridge piers, the entropic function assumes similar values, which can be identified as “undisturbed” values. The variability of such undisturbed values of  ϕ ( M ) with the flow rate is relatively small, as all the values fall in the range 0.65 < ϕ ( M ) < 0.75 , in agreement with the range found by Bahmanpouri et al. (2022b) for similar European rivers. By contrast, at cross-sections 2 and 3, just downstream of the bridge, the values of  ϕ ( M ) are consistently reduced due to the effect of the bridge. In the largest flood event of 2012, which produced near-pressure flow conditions at the bridge with marked localized increasing of the flow velocity, ϕ ( M ) CFD  equals 0.415 at cross-section 2, corresponding to M CFD = - 1.03 . The low value of  ϕ ( M ) and the negative value of  M attest the markedly non-uniform distribution of the velocity (i.e., the maximum velocity in this cross-section is much higher than the average velocity). A sensible reduction is still present 100 m downstream of the bridge (cross-section 3). For the moderate peak flows of 2019 and 2022 events, the entropic function recovers undisturbed values already at cross-section 3, i.e., 100 m downstream of the bridge.

This first analysis suggests that assuming constant values of  ϕ ( M ) can be reasonable in undisturbed river reaches; however, in the case of irregular flow fields induced by the interaction with in-stream structures, the entropic function  ϕ ( M ) can vary with respect to undisturbed values, and, in addition, it can show significant variations with the flow rate.

Table 3 Comparison between 3D-CFD outputs and entropy-based estimations forced with the river-wide distribution of the free-surface velocity.

Figure 5 Flood event of 2019, cross-section 3 (100 m downstream of the bridge). Velocity distributions provided by (a)  the 3D-CFD model and (b)  the entropy model forced with the river-wide distribution of the free-surface velocity. Comparison of vertical distributions of velocity at 0.2  B   (c) , 0.5  B   (d) , and 0.8  B   (e) , where B  is the width of the cross-section.

Figure 6 Flood event of 2019, cross-section 4 (200 m downstream of the bridge). Velocity distributions provided by (a)  the 3D-CFD model and (b)  the entropy model forced with the river-wide distribution of the free-surface velocity. Comparison of vertical distributions of velocity at 0.2  B   (c) , 0.5  B   (d) , and 0.8  B   (e) , where B  is the width of the cross-section.

3.2  Entropy model forced with the river-wide profile of free-surface velocity

The efficacy of the entropy model is tested here for the case in which the surface velocity is known for all the width of the cross-section. This could be the case in which the river-wide surface velocity is estimated from imaging techniques (e.g., Eltner et al., 2020; Schweitzer and Cowen, 2021). The results, in terms of cross-sectional velocity distributions, are presented for brevity only for the intermediate peak flow of the 2019 flood event and for the most challenging cross-sections just downstream of the bridge, where the flow field is disturbed by the pier wakes. The same results, for the peak flows of 2012 and 2022 events, are provided in the Supplement.

Figure 7 Flood event of 2012, cross-section 1 (50 m upstream of the bridge). Cross-sectional velocity distribution computed with the 3D-CFD model  (a) . Entropy theory with parabolic spanwise velocity distribution  (b) and entropy theory with elliptic spanwise velocity distribution  (c) .

Figure 4 presents the cross-sectional velocity distribution 50 m downstream of the bridge (cross-section 2). As shown by the 3D-CFD flow field (Fig. 4a) and reflected in the low value of  ϕ ( M ) for this cross-section (Table 2 and Fig. 3), the effect of the piers is very strong, such that there is a clearly uneven distribution of the cross-sectional velocity because of the wakes developing downstream of the piers. Just downstream of the bridge, due to the presence of the bridge arches, the flow field provided by the 3D-CFD model is configured as a sort of partial orifice flow that increases the vertical uniformity of the velocity distribution compared to a uniform shear flow. Of course, the entropy model cannot capture such localized flow features, which entails some difference in the patchiness of the physics-based and the entropy velocity distributions (Fig. 4a–e). Despite that, using the river-wide distribution of the surface velocity provided by the CFD simulation as input, the entropy model can reliably capture the salient features of the cross-sectional velocity distribution. Figure 4c–e highlight the comparison of 3D-CFD and entropy flow velocities along three verticals located at 0.2, 0.5, and 0.8  B (where B  is the channel width). Compared to the results of the 3D-CFD model, the entropy approach underestimates the velocity close to the bed. Since the velocities and the volumetric fluxes are still relatively small near the bed, these discrepancies marginally affect the estimation of the section-averaged velocity and, consequently, of the total discharge (Table 3). The percentage error is larger (7.6 %) for the very high-flow condition of the 2012 event (see Supplement), due to the accentuation of orifice-flow conditions associated with the higher water levels.

Figure 8 Flood event of 2012, cross-section 1 (50 m upstream of the bridge). Spanwise distribution of the surface velocity  (a) and comparison of vertical distributions of velocity at 0.2  B   (b) , 0.5  B   (c) , and 0.8  B   (d) .

Figure 5 depicts the cross-sectional velocity distributions at a larger distance from the bridge, i.e., at cross-section 3, placed 100 m downstream of the bridge. The visual comparison with Fig. 4 suggests that the effects of the piers on the flow field are reduced because of the increased distance, and the cross-sectional distribution provided by the 3D-CFD model (Fig. 5a) appears to be more regular. The statistical analysis confirms that in this case the entropy model (Fig. 5b) is able to simulate the velocity profiles with a higher accuracy.

Figure 6 shows the cross-sectional velocity distributions of 3D-CFD and entropy models for cross-section 4, located 200 m downstream of the bridge. Compared to cross-section 3, the effect of the bridge piers is further reduced because of both the distance and the more compact shape of the cross-section. Since the effect of the bridge piers is minimum, the statistical analysis shows a better agreement of the entropy model results with the CFD-based data. Though areas with relatively high velocities are still visible in simulations with higher values of the discharge (i.e., events of 2012 and 2019), for the high-flow conditions of 2022, the effect of the bridge pier has completely vanished. Therefore, the lower the flow discharge, the lower the distance from the bridge to recover undisturbed flow conditions.

The results presented here show that, when the river-wide distribution of the free-surface velocity is provided, the entropy method provides good estimations of the cross-sectional velocity distribution even when the influence of bridge piers, and thus the unevenness of the flow field, is relevant. The main discrepancies are observed in low-velocity regions, which slightly affect the estimation of the flow discharge. Table 3 lists some statistics and error percentages for the depth-averaged velocity and discharge estimations for all cross-sections and the three events considered. The estimations provided by the entropy method are in good agreement with results of CFD model, both upstream and downstream of the Adunata bridge. Though the accuracy is slightly reduced downstream of the bridge, the results are also reliable in the vicinity of the structure (i.e., at cross-section 2), suggesting the applicability of the entropy model to estimate the flow discharges, even in the case of irregular distributions of the cross-sectional velocity, provided that the river-wide distribution of the surface velocity is used as input data.

Figure 9 Flood event of 2022, cross-section 4 (200 m downstream of the bridge). Cross-sectional velocity distribution computed with the 3D-CFD model  (a) . Entropy theory with parabolic spanwise velocity distribution and  (b) entropy theory with elliptic spanwise velocity distribution  (c) .

Figure 10 Flood event of 2022, cross-section 4 (200 m downstream of the bridge). Spanwise distribution of the surface velocity  (a) and comparison of vertical distributions of velocity at 0.2  B   (b) , 0.5  B   (c) , and 0.8  B   (d) .

3.3  Entropy model forced with a single value of free-surface velocity

In this section, the results are presented considering only a single value of the surface velocity as input for the entropy model, which corresponds to the maximum surface velocity predicted by the 3D-CFD model. Two different spanwise velocity distributions are enforced in the entropic model, namely a parabolic spanwise distribution (PSD) and an elliptic spanwise distribution (ESD). Of course, applying the entropy model using a unique value of the velocity is particularly sensitive to this value and supposes a unimodal velocity distribution in the spanwise direction. For this reason, this kind of approach cannot be used in the cross-sections immediately downstream of the bridge, where the spanwise velocity distribution is markedly irregular (see e.g., Fig. 4). Herein, the results are presented for cross-section 1, located 50 m upstream of the bridge for the high-flow condition of the 2012 event, and for cross-section 4, located 200 m downstream of the bridge, for the modest peak flow condition of the 2022 event, where the effect of bridge piers on the velocity distribution wears off in a shorter distance.

Figure 7 shows the distribution of the surface velocity based on the 3D-CFD outputs and both the PSD and ESD entropy models. The agreement of both the PSD and the ESD is generally good in the central and the right parts of the channel and less good in the left part of the channel. Here, due to the irregular bathymetry (i.e., gravel deposit), the 3D-CFD model predicts localized stagnation zones that cannot be captured by the entropy model based on a single value of the surface velocity. This is confirmed by Fig. 8, which shows the cross-sectional distribution of the surface velocity and three vertical profiles. In the perspective of estimating the flow discharge, the lateral discrepancies represent a minor limit, as the central part of the cross-sections conveys the largest part of the total discharge.

Table 4 Comparison between 3D-CFD and entropy-based outputs considering a single surface velocity.

Overall, the cross-sectional velocity distributions based on ESD seem more accurate than those based on the PSD: they provide similar results at the center of the channel, but the parabolic distribution generally underestimates the flow velocity close to the banks. Both cross-sectional and vertical distributions of the velocity profiles (Figs. 7a and 8c) highlight the existence of a velocity dip; i.e., the maximum velocity is below the water surface, particularly at the center of the channel. This is generally the consequence of secondary currents superposed on the main flow (Termini and Moramarco, 2020). Yang et al. (2004) and Moramarco et al. (2017) reported that for large aspect ratios of channel flow,  B / D , the dip phenomenon appears primarily near the sidewall region, whereas for relatively low aspect ratios ( B / D = 9.26 for cross-section 1) the velocity dip is generally located at the center of the channel (Bahmanpouri et al., 2022a, b; Kundu and Ghoshal, 2018; Moramarco et al., 2017; Termini and Moramarco, 2020). In this case, the 3D flow field from the CFD simulation shows that the dip depends on the counter-clockwise rotating secondary current generated by the upstream right-handed bend. Indeed, rotational inertia makes these curvature-induced helical flow structures propagate downstream for relatively long distances (Dominguez Ruben et al., 2021; Lazzarin and Viero, 2023; Thorne et al., 1985).

Figure 11 Flood event of 2022. Color map of the instantaneous surface velocities computed with the 3D-CFD model for the Paglia River at the Adunata bridge (aerial image from © Google Earth, 2023).

The velocity distribution at cross-section 4 (200 m downstream of the bridge) is presented in Fig. 9 for the moderate peak flow condition of the 2022 event. For this cross-section, in the 3D-CFD results (Fig. 9a), the maximum surface velocity is located on the left side of the channel, rather than at its center (this aspect is discussed in the following). Forced with the maximum water surface velocity, the entropy model reproduces the velocity field in the central part of the riverbed well. Larger discrepancies are instead observed in the lateral part of the cross-section, with the elliptic spanwise distribution (ESD) that performs slightly better than the parabolic (PSD), particularly in the right side. Figure 10 shows the cross-sectional distribution of the surface velocity and the velocity distribution along three verticals. In terms of cross-sectional average velocity and flow discharge, both the PSD and ESD produce error that are lower than 10 % (Table 4), larger than those obtained using the river-wide surface velocity as input for the entropy model.

A last point worth discussing regards the unusual cross-sectional distribution of flow velocity in Sect. 4 (Fig. 9a). The reason that the 3D-CFD model locates the maximum velocity on the left of the thalweg is the alternate vortex shedding occurring downstream of the bridge piers, which propagates beyond the last considered cross-section. This is evident in the map of instantaneous surface velocity of Fig. 11. This particular occurrence poses interesting questions on the application of the entropy model to estimate the flow discharge downstream of in-stream structures. First, the spanwise location of the maximum surface velocity is subject to a periodical shift, which prevents its correct detection by means of a fixed sensor with a small-size field of view, like the one mounted on the Adunata bridge. Secondly, marked time-varying flow fields, which occasionally (or periodically) deviate from nearly uniform flow conditions, can hardly be captured by any preset velocity distribution. To alleviate the problem, the periodic signal of surface velocity can be filtered, which is equivalent to looking at time-averaged modeled flow fields; this requires knowing the frequency of vortex shedding.

The results shown in this section confirm the general accuracy of the entropy model in predicting the cross-sectional velocity distributions. As expected, when using a single value of velocity in place of the river-wide distribution of surface velocity, the accuracy of the method slightly decreases. Provided that using a single velocity is beyond the scope of the method when the spanwise velocity distribution is markedly irregular, the entropy approach can still be forced with a single surface velocity and produce accurate results, when there is no evidence of strong disturbances of the flow. Indeed, such an approach cannot capture marked unevenness in the flow field, as shown in the case of the lateral low-velocity regions at cross-section 1 for the 2012 event (Fig. 7) and in the time-varying flow field of cross-section 4 for the 2022 event (Fig. 9).

The present study investigated the ability of the entropy-based method to estimate the cross-sectional distribution of velocity, as well as the associated river discharge, for different flow conditions in a representative case study. As sensors for continuous monitoring of water level and surface velocity are often mounted on bridges, we analyzed a stretch of the Paglia River where a multi-arch bridge with thick piers, hosting a level gauge and a radar sensor, strongly affects the flow field. A 3D-CFD model was set up to obtain reliable, physics-based velocity distributions at relevant cross-sections, both upstream and downstream of the bridge. The entropy model was then applied to reproduce this set of velocity distributions, using the bathymetric data and the CFD-computed surface velocity as input data.

As a first point, the study highlighted the potential of using accurate, physics-based 3D-CFD models to deepen the knowledge of rivers and, specifically, of theoretical methods for discharge estimation. Indeed, 3D-CFD models provide pictures of complex flow fields that are more complete than, e.g., ADCP measures, in terms of spatial and temporal distribution and, above all, valid for high-flow regimes, which typically prevent any direct measurement of the flow field beneath the free surface. This entails unexplored chances of outlining best practices in the use of simplified methods for continuous discharge monitoring and, as a consequence, to improve their accuracy.

According to the present analysis, the entropy model revealed remarkable skills in also reproducing disturbed and uneven flow fields when the river-wide distribution of the surface velocity is used as input data. This occurred also just downstream of the bridge, where the pier-induced wakes made the velocity distribution multimodal and extremely irregular, with error on discharge estimates lower than 8 %. The availability of innovative measuring techniques, able to collect river-wide surface velocity data at a relatively low cost, adds value to the present findings.

On the other side, the accuracy of the entropy model is reduced when only the maximum surface velocity is used as input data, so that the spanwise velocity distribution has to be assumed on a theoretical basis (e.g., parabolic or elliptical). While such a method is absolutely discouraged in the case of disturbed flow fields (e.g., downstream of in-stream structures), it still provides accurate estimates when the velocity field is sufficiently smooth.

As a final recommendation, measuring instruments and sensors for surface velocity become more effective when placed upstream of in-stream structures, i.e., where the flow field is only marginally affected by the structure and both the water surface elevation and the velocity distribution are far more regular.

A main limitation of the present methodological approach is that it relies in the assumption of a fixed bed in both the CFD analysis and the application of the entropic model. In natural rivers, bed scouring during severe flood events and the ensuing formation of local deposits, especially close to in-stream structures such as bridges, can alter the bathymetry and, in turn, the velocity distribution and the discharge estimates. In the case of a movable bed and in the absence of protection measures (e.g., riprap or bed sills), the uncertainty associated with the local bed mobility has to be evaluated with due care. Future research on more complex scenarios that still need a comprehensive assessment, and which could largely benefit from physics-based numerical modeling, will include the case of mobile beds and the analysis of stage-dependent variations of cross-sectional velocity distribution, particularly in the case of compound cross-sections that are typical of lowland natural rivers.

To impose the boundary conditions in the 3D-CFD model, a 2D depth-averaged model of a longer stretch of the Paglia River has been set up. We used the 2DEF finite-element model (Defina, 2003; Lazzarin et al., 2023a, 2024c; Viero, 2019; Viero et al., 2013, 2014), which solves a modified version of the shallow water equations (SWEs) that allow for a robust treatment of wetting and drying over irregular topographies (D'Alpaos and Defina, 2007; Defina, 2000). The SWEs are written as

in which h s  is the free surface elevation; t  is the time; ∇  and ∇⋅  denote the 2D gradient and divergence operators, respectively; q = ( q x ; q y ) is the depth-integrated velocity (i.e., the unit-width discharge); Y  is the equivalent water depth (i.e., the volume of water per unit area); η ( h s )  is a storativity coefficient to account for the wetted fraction of the domain; τ = ( τ x ; τ y )  is the bed shear stress, evaluated using the Gauckler–Strickler formula; ρ  is the water density; and R e  is the horizontal components of the Reynolds stresses, modeled according to the Boussinesq approximation. A mixed Eulerian–Lagrangian approach allows the total derivative of the flow velocity in the momentum equations to be evaluated using finite differences and a backward tracing technique based on the method of characteristics (Defina, 2003; Giraldo, 2003; Walters and Casulli, 1998). Then, the SWEs are solved with a finite-element method, based on triangular, unstructured grids. The model also allows 2D triangular elements to be coupled with 1D elements (either open or closed sections) to model the minor hydraulic network efficiently; other 1D elements are used to model particular devices, such as pumps and weirs (Martini et al., 2004). The model has been successfully used to simulate flows in various rivers (e.g., Mel et al., 2020a, b; Viero et al., 2019; Baldasso et al., 2023); its effectiveness have also been demonstrated in different research fields, such as lagoon and marine environments (e.g., Carniello et al., 2012; Pivato et al., 2020; Tognin et al., 2022; Viero and Defina, 2016).

In the present case, the computational mesh covered a stretch of the Paglia River about 7 km long, from 600 m upstream of the Adunata bridge to the confluence with the Tiber River, including floodable floodplains (Fig. A1). The average mesh size ranged from 10 m in the riverbed near the Adunata bridge to 30 m in the floodplains and far downstream of the Adunata bridge. The computational mesh included 61 000 triangular elements, 16 1D elements to simulate underpasses, and 4 1D weir elements to simulate the sill located 500 m downstream of the Adunata bridge.

Figure A1 Spatial extent of the 2D computational mesh (aerial image from World Imagery). The color map shows the bottom elevation of the grid elements derived from the lidar-based DTM.

The inflow hydrographs, prescribed at the upstream mesh inlet, were derived from water levels measured at the Adunata bridge using the associated rating curve. At the outlet, an arbitrary rating curve was applied as the downstream boundary condition; a sensitivity analysis showed that, because of the distance from the Adunata bridge, this boundary condition did not produce any perceivable effect in the water levels simulated at the study site.

Figure A2 Observed (red) and predicted (blue) water levels at the Adunata bridge gauging station for the flood events of 2019  (a) and 2022  (b) . Observed and predicted water velocity for the flood events of 2019  (c) and 2022  (d) .

Different Gauckler–Strickler coefficients were assigned to the different parts of the domain (e.g., floodplains and densely vegetated areas) based on the soil cover. The value assigned to the main riverbed were calibrated to match the time series of the water levels measured at the Adunata bridge gauging station for the 2019 flood event (Fig. A2a), and, for the most severe flood event that occurred in 2012, the model results were also checked in terms of extent of flooded areas. The minor flood of 2022 was used to verify the model (Fig. A2b). Finally, the depth-averaged velocity just downstream of the Adunata bridge was compared with the free-surface velocity measured by the radar sensor. Due to the use of a coarse grid and to the depth-average assumption, the 2D model underpredicted the measured water surface systematically (Fig. A2c and d); however, using an amplification factor of 1.7 (gray dots in Fig. A2c and d), the predicted values were quite similar to the measured ones.

Data are available on request from the authors.

The supplement related to this article is available online at:  https://doi.org/10.5194/hess-28-3717-2024-supplement .

Conceptualization: FB, TL, SB, TM, DPV. Formal analysis: FB and TL. Funding acquisition: TM. Investigation: FB and TL. Methodology: FB, TL, SB, TM, DPV. Project administration: SB, TM, DPV. Software: FB, TL, TM, DPV. Supervision: SB, TM, DPV. Visualization: FB, TL, DPV. Writing (original draft preparation): FB. Writing (review and editing): TL, SB, TM, DPV.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

The authors acknowledge the assistance of Luigi di Micco, Shiva Rezazadeh, and Marco Dionigi.

This study was supported by the Italian National Research Program PRIN 2017 (project no. 2017SEB7Z8), “IntEractions between hydrodyNamics and bioTic communities in fluvial Ecosystems: advancement in the knowledge and undeRstanding of PRocesses and ecosystem sustainability by the development of novel technologieS with fIeld monitoriNg and laboratory testing (ENTERPRISING)”. Tommaso Lazzarin is sponsored by a scholarship provided by the CARIPARO Foundation.

This paper was edited by Alberto Guadagnini and reviewed by Gustavo Marini and two anonymous referees.

Abdolvandi, A. F., Ziaei, A. N., Moramarco, T., and Singh, V. P.: New approach to computing mean velocity and discharge, Hydrolog. Sci. J., 66, 347–353, https://doi.org/10.1080/02626667.2020.1859115 , 2021. 

Ammari, A., Bahmanpouri, F., Khelfi, M. E. A., and Moramarco, T.: The regionalizing of the entropy parameter over the north Algerian watersheds: a discharge measurement approach for ungauged river sites, Hydrolog. Sci. J., 67, 1640–1655, https://doi.org/10.1080/02626667.2022.2099744 , 2022. 

Ataie-Ashtiani, B. and Aslani-Kordkandi, A.: Flow field around side-by-side piers with and without a scour hole, Eur. J. Mech. B, 36, 152–166, https://doi.org/10.1016/j.euromechflu.2012.03.007 , 2012. 

Bahmanpouri, F., Eltner, A., Barbetta, S., Bertalan, L., and Moramarco, T.: Estimating the Average River Cross-Section Velocity by Observing Only One Surface Velocity Value and Calibrating the Entropic Parameter, Water Resour. Res., 58, e2021WR031821, https://doi.org/10.1029/2021WR031821 , 2022a. 

Bahmanpouri, F., Barbetta, S., Gualtieri, C., Ianniruberto, M., Filizola, N., Termini, D., and Moramarco, T.: Prediction of river discharges at confluences based on Entropy theory and surface-velocity measurements, J. Hydrol., 606, 127404, https://doi.org/10.1016/j.jhydrol.2021.127404 , 2022b. 

Baldasso, F., Tognin, D., Lazzarin, T., and Viero, D. P.: The role of morphodynamic processes on the Po river conveyance downstream of Pontelagoscuro: a numerical analysis, L'Acqua, 4/2023, https://www.idrotecnicaitaliana.it/ (last access: 8 August 2024), 2023. 

Bandini, F., Sunding, T. P., Linde, J., Smith, O., Jensen, I. K., Köppl, C. J., Butts, M., and Bauer-Gottwein, P.: Unmanned Aerial System (UAS) observations of water surface elevation in a small stream: Comparison of radar altimetry, LIDAR and photogrammetry techniques, Remote Sens. Environ., 237, 111487, https://doi.org/10.1016/j.rse.2019.111487 , 2020. 

Bandini, F., Lüthi, B., Peña-Haro, S., Borst, C., Liu, J., Karagkiolidou, S., Hu, X., Lemaire, G. G., Bjerg, P. L., and Bauer-Gottwein, P.: A Drone-Borne Method to Jointly Estimate Discharge and Manning's Roughness of Natural Streams, Water Resour. Res., 57, e2020WR028266, https://doi.org/10.1029/2020WR028266 , 2021. 

Barbetta, S., Camici, S., and Moramarco, T.: A reappraisal of bridge piers scour vulnerability: a case study in the Upper Tiber River basin (central Italy), J. Flood Risk Manage., 10, 283–300, https://doi.org/10.1111/jfr3.12130 , 2017. 

Bogning, S., Frappart, F., Blarel, F., Niño, F., Mahé, G., Bricquet, J.-P., Seyler, F., Onguéné, R., Etamé, J., Paiz, M.-C., and Braun, J.-J.: Monitoring Water Levels and Discharges Using Radar Altimetry in an Ungauged River Basin: The Case of the Ogooué, Remote Sens., 10, 350, https://doi.org/10.3390/rs10020350 , 2018. 

Bonakdari, H., Larrarte, F., Lassabatere, L., and Joannis, C.: Turbulent velocity profile in fully-developed open channel flows, Environ. Fluid Mech., 8, 1–17, https://doi.org/10.1007/s10652-007-9051-6 , 2008. 

Bonakdari, H., Sheikh, Z., and Tooshmalani, M.: Comparison between Shannon and Tsallis entropies for prediction of shear stress distribution in open channels, Stoch. Environ. Res. Risk A., 29, 1–11, https://doi.org/10.1007/s00477-014-0959-3 , 2015. 

Briaud, J. L., Chen, H. C., Chang, K. A., Oh, S. J., and Chen, X.: Abutment scour in cohesive materials, NCHRP Report 24-15(2), Transportation Research Board, National Research Council, Washington, D.C., USA, https://onlinepubs.trb.org/onlinepubs/nchrp/docs/NCHRP24-15(2)_FR.pdf (last access: 8 August 2024), 2009. 

Carniello, L., Defina, A., and D'Alpaos, L.: Modeling sand-mud transport induced by tidal currents and wind waves in shallow microtidal basins: Application to the Venice Lagoon (Italy), Estuar. Coast. Shelf Sci., 102–103, 105–115, https://doi.org/10.1016/j.ecss.2012.03.016 , 2012. 

Chahrour, N., Castaings, W., and Barthélemy, E.: Image-based river discharge estimation by merging heterogeneous data wit h information entropy theory, Flow Meas. Instrum., 81, 102039, https://doi.org/10.1016/j.flowmeasinst.2021.102039 , 2021. 

Chang, W.-Y., Constantinescu, G., Lien, H.-C., Tsai, W.-F., Lai, J.-S., and Loh, C.-H.: Flow Structure around Bridge Piers of Varying Geometrical Complexity, J. Hydraul. Eng.-ASCE, 139, 812–826, https://doi.org/10.1061/(ASCE)HY.1943-7900.0000742 , 2013. 

Cheng, Z., Koken, M., and Constantinescu, G.: Approximate methodology to account for effects of coherent structures on sediment entrainment in RANS simulations with a movable bed and applications to pier scour, Adv. Water Resour., 120, 65–82, https://doi.org/10.1016/j.advwatres.2017.05.019 , 2018. 

Chiu, C.-L.: Entropy and Probability Concepts in Hydraulics, J. Hydraul. Eng.-ASCE, 113, 583–599, https://doi.org/10.1061/(ASCE)0733-9429(1987)113:5(583) , 1987. 

Chiu, C.-L.: Entropy and 2-D Velocity Distribution in Open Channels, J. Hydraul. Eng.-ASCE, 114, 738–756, https://doi.org/10.1061/(ASCE)0733-9429(1988)114:7(738) , 1988. 

Chiu, C.-L.: Velocity Distribution in Open Channel Flow, J. Hydraul. Eng.-ASCE, 115, 576–594, https://doi.org/10.1061/(ASCE)0733-9429(1989)115:5(576) , 1989. 

Chiu, C.-L.: Application of Entropy Concept in Open-Channel Flow Study, J. Hydraul. Eng.-ASCE, 117, 615–628, https://doi.org/10.1061/(ASCE)0733-9429(1991)117:5(615) , 1991. 

Chiu, C.-L. and Murray, D. W.: Variation of Velocity Distribution along Nonuniform Open-Channel Flow, J. Hydraul. Eng.-ASCE, 118, 989–1001, https://doi.org/10.1061/(ASCE)0733-9429(1992)118:7(989) , 1992. 

Chiu, C.-L. and Said, C. A. A.: Maximum and Mean Velocities and Entropy in Open-Channel Flow, J. Hydraul. Eng.-ASCE, 121, 26–35, https://doi.org/10.1061/(ASCE)0733-9429(1995)121:1(26) , 1995. 

Chiu, C.-L., Hsu, S.-M., and Tung, N.-C.: Efficient methods of discharge measurements in rivers and streams based on the probability concept, Hydrol. Process., 19, 3935–3946, https://doi.org/10.1002/hyp.5857 , 2005. 

Constantinescu, G., Koken, M., and Zeng, J.: The structure of turbulent flow in an open channel bend of strong curvature with deformed bed: Insight provided by detached eddy simulation, Water Resour. Res., 47, W05515, https://doi.org/10.1029/2010WR010114 , 2011. 

Constantinescu, G., Kashyap, S., Tokyay, T., Rennie, C. D., and Townsend, R. D.: Hydrodynamic processes and sediment erosion mechanisms in an open channel bend of strong curvature with deformed bathymetry, J. Geophys. Res.-Earth, 118, 480–496, https://doi.org/10.1002/jgrf.20042 , 2013. 

D'Alpaos, L. and Defina, A.: Mathematical modeling of tidal hydrodynamics in shallow lagoons: A review of open issues and applications to the Venice lagoon, Comput. Geosci., 33, 476–496, https://doi.org/10.1016/j.cageo.2006.07.009 , 2007. 

Defina, A.: Two-dimensional shallow flow equations for partially dry areas, Water Resour. Res., 36, 3251–3264, https://doi.org/10.1029/2000WR900167 , 2000. 

Defina, A.: Numerical experiments on bar growth, Water Resour. Res., 39, 1092, https://doi.org/10.1029/2002WR001455 , 2003. 

Depetris, P. J.: The Importance of Monitoring River Water Discharge, Front. Water, 3, 745912, https://doi.org/10.3389/frwa.2021.745912 , 2021. 

Di Baldassarre, G. and Montanari, A.: Uncertainty in river discharge observations: a quantitative analysis, Hydrol. Earth Syst. Sci., 13, 913–921, https://doi.org/10.5194/hess-13-913-2009 , 2009. 

Dominguez Ruben, L., Szupiany, R. N., Tassi, P., and Vionnet, C. A.: Large meandering bends with high width-to-depth ratios: Insights from hydro-sedimentological processes, Geomorphology, 374, 107521, https://doi.org/10.1016/j.geomorph.2020.107521 , 2021. 

Dottori, F., Di Baldassarre, G., and Todini, E.: Detailed data is welcome, but with a pinch of salt: Accuracy, precision, and uncertainty in flood inundation modeling, Water Resour. Res., 49, 6079–6085, https://doi.org/10.1002/wrcr.20406 , 2013. 

Ebtehaj, I., Bonakdari, H., Moradi, F., Gharabaghi, B., and Khozani, Z. S.: An integrated framework of Extreme Learning Machines for predicting scour at pile groups in clear water condition, Coast. Eng., 135, 1–15, https://doi.org/10.1016/j.coastaleng.2017.12.012 , 2018. 

Eltner, A., Sardemann, H., and Grundmann, J.: Technical Note: Flow velocity and discharge measurement in rivers using terrestrial and unmanned-aerial-vehicle imagery, Hydrol. Earth Syst. Sci., 24, 1429–1445, https://doi.org/10.5194/hess-24-1429-2020 , 2020. 

Federico, F., Silvagni, G., and Volpi, F.: Scour Vulnerability of River Bridge Piers, J. Geotech. Geoenviron. Eng., 129, 890–899, https://doi.org/10.1061/(ASCE)1090-0241(2003)129:10(890) , 2003. 

Fekete, B. M. and Vörösmarty, C. J.: The current status of global river discharge monitoring and potential new technologies complementing traditional discharge measurements, Brasilia, 20–22 November 2002, 309, 129–136, 2002. 

Fekete, B. M., Looser, U., Pietroniro, A., and Robarts, R. D.: Rationale for Monitoring Discharge on the Ground, J. Hydrometeorol., 13, 1977–1986, https://doi.org/10.1175/JHM-D-11-0126.1 , 2012. 

Ferro, V.: ADV measurements of velocity distributions in a gravel-bed flume, Earth Surf. Proc. Land., 28, 707–722, https://doi.org/10.1002/esp.467 , 2003. 

Franca, M. J., Ferreira, R. M. L., and Lemmin, U.: Parameterization of the logarithmic layer of double-averaged streamwise velocity profiles in gravel-bed river flows, Adv. Water Resour., 31, 915–925, https://doi.org/10.1016/j.advwatres.2008.03.001 , 2008. 

Fujita, I., Watanabe, H., and Tsubaki, R.: Development of a non-intrusive and efficient flow monitoring technique: The space-time image velocimetry (STIV), Int. J. River Basin Manage., 5, 105–114, https://doi.org/10.1080/15715124.2007.9635310 , 2007. 

Fujita, I., Notoya, Y., Tani, K., and Tateguchi, S.: Efficient and accurate estimation of water surface velocity in STIV, Environ. Fluid Mech., 19, 1363–1378, https://doi.org/10.1007/s10652-018-9651-3 , 2019. 

Fulton, J. and Ostrowski, J.: Measuring real-time streamflow using emerging technologies: Radar, hydroacoustics, and the probability concept, J. Hydrol., 357, 1–10, https://doi.org/10.1016/j.jhydrol.2008.03.028 , 2008. 

Giraldo, F. X.: Strong and weak Lagrange-Galerkin spectral element methods for the shallow water equations, Comput. Math. Appl., 45, 97–121, https://doi.org/10.1016/S0898-1221(03)80010-X , 2003. 

Gore, J. A. and Banning, J.: Chapter 3 – Discharge Measurements and Streamflow Analysis, in: Methods in Stream Ecology, Volume 1, 3rd Edn., edited by: Hauer, F. R. and Lamberti, G. A., Academic Press, Boston, 49–70, https://doi.org/10.1016/B978-0-12-416558-8.00003-2 , 2017. 

Guo, J.: Modified log-wake-law for smooth rectangular open channel flow, J. Hydraul. Res., 52, 121–128, https://doi.org/10.1080/00221686.2013.818584 , 2014. 

Herschy, R. W.: Streamflow Measurement, in: 3rd Edn., CRC Press, https://doi.org/10.1201/9781482265880 , 2009. 

Hirt, C. W. and Nichols, B. D.: Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39, 201–225, https://doi.org/10.1016/0021-9991(81)90145-5 , 1981. 

Horna-Munoz, D. and Constantinescu, G.: A fully 3-D numerical model to predict flood wave propagation and assess efficiency of flood protection measures, Adv. Water Resour., 122, 148–165, https://doi.org/10.1016/j.advwatres.2018.10.014 , 2018. 

Jodeau, M., Hauet, A., Paquier, A., Le Coz, J., and Dramais, G.: Application and evaluation of LS-PIV technique for the monitoring of river surface velocities in high flow conditions, Flow Meas. Instrum., 19, 117–127, https://doi.org/10.1016/j.flowmeasinst.2007.11.004 , 2008. 

Kästner, K., Hoitink, A. J. F., Torfs, P. J. J. F., Vermeulen, B., Ningsih, N. S., and Pramulya, M.: Prerequisites for Accurate Monitoring of River Discharge Based on Fixed-Location Velocity Measurements, Water Resour. Res., 54, 1058–1076, https://doi.org/10.1002/2017WR020990 , 2018. 

Khosronejad, A., Kang, S., and Sotiropoulos, F.: Experimental and computational investigation of local scour around bridge piers, Adv. Water Resour., 37, 73–85, https://doi.org/10.1016/j.advwatres.2011.09.013 , 2012. 

Kirkil, G. and Constantinescu, G.: Effects of cylinder Reynolds number on the turbulent horseshoe vortex system and near wake of a surface-mounted circular cylinder, Phys. Fluids, 27, 075102, https://doi.org/10.1063/1.4923063 , 2015. 

Kirkil, G., Constantinescu, G., and Ettema, R.: Detached Eddy Simulation Investigation of Turbulence at a Circular Pier with Scour Hole, J. Hydraul. Eng.-ASCE, 135, 888–901, https://doi.org/10.1061/(ASCE)HY.1943-7900.0000101 , 2009. 

Koken, M., Constantinescu, G., and Blanckaert, K.: Hydrodynamic processes, sediment erosion mechanisms, and Reynolds-number-induced scale effects in an open channel bend of strong curvature with flat bathymetry, J. Geophys. Res.-Earth, 118, 2308–2324, https://doi.org/10.1002/2013JF002760 , 2013. 

Kundu, S. and Ghoshal, K.: An Entropy Based Model for Velocity-Dip-Position, J. Environ. Inform., 33, 113–128, 2018. 

Laursen, E. M.: Scour at Bridge Crossings, J. Hydraul. Div., 86, 39–54, https://doi.org/10.1061/JYCEAJ.0000426 , 1960. 

Laursen, E. M.: An Analysis of Relief Bridge Scour, J. Hydraul. Div., 89, 93–118, https://doi.org/10.1061/JYCEAJ.0000896 , 1963. 

Lazzarin, T. and Viero, D. P.: Curvature-induced secondary flow in 2D depth-averaged hydro-morphodynamic models: An assessment of different approaches and key factors, Adv. Water Resour., 171, 104355, https://doi.org/10.1016/j.advwatres.2022.104355 , 2023. 

Lazzarin, T., Defina, A., and Viero, D. P.: Assessing 40 Years of Flood Risk Evolution at the Micro-Scale Using an Innovative Modeling Approach: The Effects of Urbanization and Land Planning, Geosciences, 13, 112, https://doi.org/10.3390/geosciences13040112 , 2023a. 

Lazzarin, T., Viero, D. P., Defina, A., and Cozzolino, L.: Flow under vertical sluice gates: Flow stability at large gate opening and disambiguation of partial dam-break multiple solutions, Phys. Fluids, 35, 024114, https://doi.org/10.1063/5.0131953 , 2023b. 

Lazzarin, T., Constantinescu, G., Di Micco, L., Wu, H., Lavignani, F., Lo Brutto, M., Termini, D., and Viero, D. P.: Influence of bed roughness on flow and turbulence structure around a partially-buried, isolated freshwater mussel, Water Resour. Res., 59, e2022WR034151, https://doi.org/10.1029/2022WR034151 , 2023c. 

Lazzarin, T., Constantinescu, G., and Viero, D. P.: A numerical investigation of flow field and bed stresses at a river bridge: the effects of piers and of pressure-flow with deck overtopping, J. Hydraul. Eng., under review, 2024a. 

Lazzarin, T., Constantinescu, G., Wu, H., and Viero, D. P.: Fully Developed Open Channel Flow over Clusters of Freshwater Mussels Partially Buried in a Gravel Bed, Water Resour. Res., 60, e2023WR035594, https://doi.org/10.1029/2023WR035594 , 2024b. 

Lazzarin, T., Chen, A. S., and Viero, D. P.: Beyond flood hazard. Mapping the loss probability of pedestrians to improve risk estimation and communication, Sci. Total Environ., 912, 168718, https://doi.org/10.1016/j.scitotenv.2023.168718 , 2024c. 

Le Coz, J., Hauet, A., Pierrefeu, G., Dramais, G., and Camenen, B.: Performance of image-based velocimetry (LSPIV) applied to flash-flood discharge measurements in Mediterranean rivers, J. Hydrol., 394, 42–52, https://doi.org/10.1016/j.jhydrol.2010.05.049 , 2010. 

Li, B. and Zhang, X.: Evolution of outer bank cell in open-channel bends, Environ. Fluid Mech., 22, 715–742, https://doi.org/10.1007/s10652-022-09865-2 , 2022. 

Lu, B., Petukhov, V., Zhang, M., Wang, X., Yue, S., Zhou, H., Kholodov, A., and Yu, G.: Prediction of flow-induced local scour depth at the uniform bridge pier using masked attention neural network, Ocean Eng., 266, 113018, https://doi.org/10.1016/j.oceaneng.2022.113018 , 2022. 

Luo, H., Fytanidis, D. K., Schmidt, A. R., and García, M. H.: Comparative 1D and 3D numerical investigation of open-channel junction flows and energy losses, Adv. Water Resour., 117, 120–139, https://doi.org/10.1016/j.advwatres.2018.05.012 , 2018. 

Marini, G. and Fontana, N.: Mean Velocity and Entropy in Wide Channel Flows, J. Hydrol. Eng.-ASCE, 25, 06019009, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001870 , 2020. 

Martini, P., Carniello, L., and Avanzi, C.: Two dimensional modelling of flood flows and suspended sedimenttransport: the case of the Brenta River, Veneto (Italy), Nat. Hazards Earth Syst. Sci., 4, 165–181, https://doi.org/10.5194/nhess-4-165-2004 , 2004. 

Meals, D. W. and Dressing, S. A.: Surface water flow measurement for water quality monitoring projects, Tech Notes 3, March 2008. Developed for U.S. Environmental Protection Agency by Tetra Tech, Inc., Fairfax, VA, 16 p. https://www.epa.gov/polluted-runoff-nonpoint-source-pollution/nonpointsource-monitoring-technical-notes (last access: 8 August 2024), 2008. 

Mel, R. A., Viero, D. P., Carniello, L., and D'Alpaos, L.: Multipurpose Use of Artificial Channel Networks for Flood Risk Reduction: The Case of the Waterway Padova–Venice (Italy), Water, 12, 1609, https://doi.org/10.3390/w12061609 , 2020a. 

Mel, R. A., Viero, D. P., Carniello, L., and D'Alpaos, L.: Optimal floodgate operation for river flood management: The case study of Padova (Italy), J. Hydrol.: Reg. Stud., 30, 100702, https://doi.org/10.1016/j.ejrh.2020.100702 , 2020b. 

Moramarco, T. and Singh, V. P.: Formulation of the Entropy Parameter Based on Hydraulic and Geometric Characteristics of River Cross Sections, J. Hydrol. Eng.-ASCE, 15, 852–858, https://doi.org/10.1061/(ASCE)HE.1943-5584.0000255 , 2010. 

Moramarco, T., Saltalippi, C., and Singh, V. P.: Estimation of Mean Velocity in Natural Channels Based on Chiu's Velocity Distribution Equation, J. Hydrol. Eng.-ASCE, 9, 42–50, https://doi.org/10.1061/(ASCE)1084-0699(2004)9:1(42) , 2004. 

Moramarco, T., Barbetta, S., and Tarpanelli, A.: From Surface Flow Velocity Measurements to Discharge Assessment by the Entropy Theory, Water, 9, 120, https://doi.org/10.3390/w9020120 , 2017. 

Moramarco, T., Barbetta, S., Bjerklie, D. M., Fulton, J. W., and Tarpanelli, A.: River Bathymetry Estimate and Discharge Assessment from Remote Sensing, Water Resour. Res., 55, 6692–6711, https://doi.org/10.1029/2018WR024220 , 2019. 

Muste, M., Ho, H.-C., and Kim, D.: Considerations on direct stream flow measurements using video imagery: Outlook and research needs, J. Hydro-Environ. Res., 5, 289–300, https://doi.org/10.1016/j.jher.2010.11.002 , 2011. 

Muste, M., Hauet, A., Fujita, I., Legout, C., and Ho, H.-C.: Capabilities of Large-scale Particle Image Velocimetry to characterize shallow free-surface flows, Adv. Water Resour., 70, 160–171, https://doi.org/10.1016/j.advwatres.2014.04.004 , 2014. 

Nezu, I. and Nakagawa, H.: Turbulence in Open Channel Flows, Balkema, Rotterdam, the Netherlands, https://doi.org/10.1201/9780203734902 , 1993. 

Nikora, V. and Roy, A. G.: Secondary Flows in Rivers: Theoretical Framework, Recent Advances, and Current Challenges, in: Gravel-Bed Rivers, John Wiley & Sons, Ltd, 1–22, https://doi.org/10.1002/9781119952497.ch1 , 2011. 

Pilbala, A., Riccardi, N., Benistati, N., Modesto, V., Termini, D., Manca, D., Benigni, A., Corradini, C., Lazzarin, T., Moramarco, T., Fraccarollo, L., and Piccolroaz, S.: Real-time biological early-warning system based on freshwater mussels' valvometry data, Hydrol. Earth Syst. Sci., 28, 2297–2311, https://doi.org/10.5194/hess-28-2297-2024 , 2024. 

Pivato, M., Carniello, L., Viero, D. P., Soranzo, C., Defina, A., and Silvestri, S.: Remote Sensing for Optimal Estimation of Water Temperature Dynamics in Shallow Tidal Environments, Remote Sens., 12, 51, https://doi.org/10.3390/rs12010051 , 2020. 

Proust, S. and Nikora, V. I.: Compound open-channel flows: effects of transverse currents on the flow structure, J. Fluid Mech., 885, A24, https://doi.org/10.1017/jfm.2019.973 , 2020. 

Salaheldin, T. M., Imran, J., and Chaudhry, M. H.: Numerical Modeling of Three-Dimensional Flow Field Around Circular Piers, J. Hydraul. Eng.-ASCE, 130, 91–100, https://doi.org/10.1061/(ASCE)0733-9429(2004)130:2(91) , 2004. 

Schweitzer, S. A. and Cowen, E. A.: Instantaneous River-Wide Water Surface Velocity Field Measurements at Centimeter Scales Using Infrared Quantitative Image Velocimetry, Water Resour. Res., 57, e2020WR029279, https://doi.org/10.1029/2020WR029279 , 2021. 

Shih, T.-H., Liou, W. W., Shabbir, A., Yang, Z., and Zhu, J.: A new k – ϵ eddy viscosity model for high reynolds number turbulent flows, Comput. Fluids, 24, 227–238, https://doi.org/10.1016/0045-7930(94)00032-T , 1995. 

Singh, V. P., Sivakumar, B., and Cui, H.: Tsallis Entropy Theory for Modeling in Water Engineering: A Review, Entropy, 19, 641, https://doi.org/10.3390/e19120641 , 2017. 

Spada, E., Sinagra, M., Tucciarelli, T., and Biondi, D.: Unsteady State Water Level Analysis for Discharge Hydrograph Estimation in Rivers with Torrential Regime: The Case Study of the February 2016 Flood Event in the Crati River, South Italy, Water, 9, 288, https://doi.org/10.3390/w9040288 , 2017. 

Sterling, M. and Knight, D.: An attempt at using the entropy approach to predict the transverse distribution of boundary shear stress in open channel flow, Stoch. Environ. Res. Risk A., 16, 127–142, https://doi.org/10.1007/s00477-002-0088-2 , 2002. 

Sumer, B. M., Christiansen, N., and Fredsøe, J.: The horseshoe vortex and vortex shedding around a vertical wall-mounted cylinder exposed to waves, J. Fluid Mech., 332, 41–70, https://doi.org/10.1017/S0022112096003898 , 1997. 

Termini, D. and Moramarco, T.: Application of entropic approach to estimate the mean flow velocity and Manning roughness coefficient in a high-curvature flume, Hydrol. Res., 48, 634–645, https://doi.org/10.2166/nh.2016.106 , 2017. 

Termini, D. and Moramarco, T.: Entropic model application to identify cross-sectional flow effect on velocity distribution in a large amplitude meandering channel, Adv. Water Resour., 143, 103678, https://doi.org/10.1016/j.advwatres.2020.103678 , 2020. 

Thorne, C. R., Zevenbergen, L. W., Pitlick, J. C., Rais, S., Bradley, J. B., and Julien, P. Y.: Direct measurements of secondary currents in a meandering sand-bed river, Nature, 315, 746–747, https://doi.org/10.1038/315746a0 , 1985. 

Tognin, D., Finotello, A., D'Alpaos, A., Viero, D. P., Pivato, M., Mel, R. A., Defina, A., Bertuzzo, E., Marani, M., and Carniello, L.: Loss of geomorphic diversity in shallow tidal embayments promoted by storm-surge barriers, Sci. Adv., 8, eabm8446, https://doi.org/10.1126/sciadv.abm8446 , 2022. 

Vandaele, R., Dance, S. L., and Ojha, V.: Calibrated river-level estimation from river cameras using convolutional neural networks, Environ. Data Sci., 2, e11, https://doi.org/10.1017/eds.2023.6 , 2023. 

van Rijn, L. C.: Equivalent Roughness of Alluvial Bed, J. Hydraul. Div., 108, 1215–1218, https://doi.org/10.1061/JYCEAJ.0005917 , 1982. 

Viero, D. P.: Modelling urban floods using a finite element staggered scheme with an anisotropic dual porosity model, J. Hydrol., 568, 247–259, https://doi.org/10.1016/j.jhydrol.2018.10.055 , 2019. 

Viero, D. P. and Defina, A.: Water age, exposure time, and local flushing time in semi-enclosed, tidal basins with negligible freshwater inflow, J. Mar. Syst., 156, 16–29, https://doi.org/10.1016/j.jmarsys.2015.11.006 , 2016. 

Viero, D. P., D'Alpaos, A., Carniello, L., and Defina, A.: Mathematical modeling of flooding due to river bank failure, Adv. Water Resour., 59, 82–94, https://doi.org/10.1016/j.advwatres.2013.05.011 , 2013. 

Viero, D. P., Peruzzo, P., Carniello, L., and Defina, A.: Integrated mathematical modeling of hydrological and hydrodynamic response to rainfall events in rural lowland catchments, Water Resour. Res., 50, 5941–5957, https://doi.org/10.1002/2013WR014293 , 2014. 

Viero, D. P., Roder, G., Matticchio, B., Defina, A., and Tarolli, P.: Floods, landscape modifications and population dynamics in anthropogenic coastal lowlands: The Polesine (northern Italy) case study, Sci. Total Environ., 651, 1435–1450, https://doi.org/10.1016/j.scitotenv.2018.09.121 , 2019. 

Vyas, J. K., Perumal, M., and Moramarco, T.: Entropy Based River Discharge Estimation Using One-Point Velocity Measurement at 0.6D, Water Resour. Res., 57, e2021WR029825, https://doi.org/10.1029/2021WR029825 , 2021. 

Walters, R. A. and Casulli, V.: A robust, finite element model for hydrostatic surface water flows, Commun. Numer. Meth. Eng., 14, 931–940, https://doi.org/10.1002/(SICI)1099-0887(1998100)14:10<931::AID-CNM199>3.0.CO;2-X , 1998. 

Yang, S.-Q., Tan, S.-K., and Lim, S.-Y.: Velocity Distribution and Dip-Phenomenon in Smooth Uniform Open Channel Flows, J. Hydraul. Eng.-ASCE, 130, 1179–1186, https://doi.org/10.1061/(ASCE)0733-9429(2004)130:12(1179) , 2004.  

Yang, S.-Q., Tan, S. K., and Wang, X.-K.: Mechanism of secondary currents in open channel flows, J. Geophys. Res.-Earth, 117, F04014, https://doi.org/10.1029/2012JF002510 , 2012. 

Yang, Y., Xiong, X., Melville, B. W., and Sturm, T. W.: Flow Redistribution at Bridge Contractions in Compound Channel for Extreme Hydrological Events and Implications for Sediment Scour, J. Hydraul. Eng.-ASCE, 147, 04021005, https://doi.org/10.1061/(ASCE)HY.1943-7900.0001861 , 2021. 

Yoshimura, H. and Fujita, I.: Investigation of free-surface dynamics in an open-channel flow, J. Hydraul. Res., 58, 231–247, https://doi.org/10.1080/00221686.2018.1561531 , 2020. 

Zhang, Z., Zhou, Y., Liu, H., and Gao, H.: In-situ water level measurement using NIR-imaging video camera, Flow Meas. Instrum., 67, 95–106, https://doi.org/10.1016/j.flowmeasinst.2019.04.004 , 2019. 

• Introduction
• Material and methods
• Results and discussions
• Conclusions
• Data availability
• Author contributions
• Competing interests
• Acknowledgements
• Financial support
• Review statement