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• 29 Feb 2024

Beyond Goals: David Beckham's Playbook for Mobilizing Star Talent

Reach soccer's pinnacle. Become a global brand. Buy a team. Sign Lionel Messi. David Beckham makes success look as easy as his epic free kicks. But leveraging world-class talent takes discipline and deft decision-making, as case studies by Anita Elberse reveal. What could other businesses learn from his ascent?

• 26 Sep 2023
• Cold Call Podcast

The PGA Tour and LIV Golf Merger: Competition vs. Cooperation

On June 9, 2022, the first LIV Golf event teed off outside of London. The new tour offered players larger prizes, more flexibility, and ambitions to attract new fans to the sport. Immediately following the official start of that tournament, the PGA Tour announced that all 17 PGA Tour players participating in the LIV Golf event were suspended and ineligible to compete in PGA Tour events. Tensions between the two golf entities continued to rise, as more players “defected” to LIV. Eventually LIV Golf filed an antitrust lawsuit accusing the PGA Tour of anticompetitive practices, and the Department of Justice launched an investigation. Then, in a dramatic turn of events, LIV Golf and the PGA Tour announced that they were merging. Harvard Business School assistant professor Alexander MacKay discusses the competitive, antitrust, and regulatory issues at stake and whether or not the PGA Tour took the right actions in response to LIV Golf’s entry in his case, “LIV Golf.”

• 22 Nov 2022
• Research & Ideas

When Agreeing to Disagree Is a Good Beginning

When conflict stems from honest and open listening, disagreement can be a good thing, say Francesca Gino and Julia Minson. But developing those skills requires patience and discipline.

• 20 Apr 2021
• Working Paper Summaries

Cognitive Biases: Mistakes or Missing Stakes?

This study of field and lab data strongly suggests that people do not necessarily make better decisions when the stakes are very high. Results highlight the potential economic consequences of cognitive biases.

• 02 Apr 2021

Salary Negotiations: A Catch-22 for Women

Too assertive or too nice? New research from Julian Zlatev probes the lose-lose dynamics that penalize women in negotiations and perpetuate gender inequity. Open for comment; 0 Comments.

• 31 Mar 2020

Controlling the Emotion of Negotiation

Leslie John discusses the importance of asking (and answering) the right questions when negotiating, particularly under emotional stress. Open for comment; 0 Comments.

• 13 May 2019

The Unexpected Way Whistleblowers Reduce Government Fraud

Even unfounded allegations by whistleblowers can force government contractors to renegotiate their terms, say Jonas Heese and Gerardo Perez Cavazos. Open for comment; 0 Comments.

• 08 Mar 2019

Seven Negotiation Lessons from Amazon's HQ Disaster in Queens

After a lengthy courting process, Amazon thought its plan for a New York HQ campus was in the bag. But the company failed a primary goal of negotiations, says James Sebenius. Open for comment; 0 Comments.

• 15 Oct 2018

Shaky Business: How Handshakes Win Negotiations

A handshake before a negotiation can have a surprisingly strong effect on the outcome, according to Michael Norton, Francesca Gino, and colleagues. Open for comment; 0 Comments.

• 30 Jul 2018

Why Ethical People Become Unethical Negotiators

You may think you are an ethical person, but self-interest can cloud your judgment when you sit down at the bargaining table, says Max Bazerman. Open for comment; 0 Comments.

• 05 Jul 2018

Henry Kissinger's Lessons for Business Negotiators

Much has been written about Henry Kissinger the diplomat and United States secretary of state, but surprisingly little about Kissinger the dealmaker. A trio of Harvard scholars remedies that with Kissinger the Negotiator: Lessons from Dealmaking at the Highest Level. Co-author James Sebenius discusses what business negotiators can learn. Open for comment; 0 Comments.

• 23 Jan 2018

Transaction Costs and the Duration of Contracts

When buyers transact with sellers, they select not only whom to transact with but also for how long. This paper develops a model of optimal contract duration arising from underlying supply costs and transaction costs. The model allows for the quantification of transaction costs, which are often unobserved, and the impact of these costs on welfare.

• 05 Apr 2017

For Women Especially, It Pays to Know What Car Repairs Should Cost

Consumers can negotiate cheaper auto repair prices by convincing service reps they know something about market rates—helping women overcome gender discrimination, according to recently published research by Ayelet Israeli and co-authors. Open for comment; 0 Comments.

• 05 Dec 2016

How The 2016 Presidential Candidates Misled Us With Truthful Statements

Paltering, a subtle form of lying where an almost true statement is used, is not unknown in the world of politics. Here are several examples. Open for comment; 0 Comments.

How To Deceive Others With Truthful Statements (It's Called 'Paltering,' And It's Risky)

Presidential candidates do it. Business leaders do it. You probably do it, too. Paltering is a gentle form of lying, but is reviled by negotiators on the receiving end. Research by Francesca Gino, Michael Norton, and colleagues. Open for comment; 0 Comments.

• 23 May 2016

A Little Understanding Motivates Copyright Abusers to Pay Up

Many Internet users don't give a second thought to copying and reusing an image. Hong Luo and Julie Holland Mortimer explain how copyright holders can gently persuade abusers to do the right thing. Open for comment; 0 Comments.

• 11 May 2016

Fix This! Why is it so Painful to Buy a New Car?

Car-buying sends shivers up the backbones of American consumers, so why hasn’t the industry stepped up to create a better experience? Leonard Schlesinger, Jill Avery, and Ryan Buell tell their own war stories and talk about how the battle might yet be won. Open for comment; 0 Comments.

• 18 Apr 2016

The Cost of Leaning In

Women who are forced to negotiate tend to fare worse than if they hadn’t negotiated at all, according to research by Christine Exley, Muriel Niederle, and Lise Vesterlund. Open for comment; 0 Comments.

• 13 Apr 2016

Knowing When to Ask: The Cost of Leaning-in

The popular push for women to “lean in” holds that women should negotiate on their own behalf to overcome the gender wage gap. This study, however, shows the importance of choice in successful negotiations. Women usually choose to enter negotiations leading to financial gains and avoid negotiations that would result in financial losses. Regardless of the reasons for avoidance, leaning-in is not automatically the best advice for women.

• 04 Apr 2016

How to Negotiate Situations That Feel Hopeless

In Negotiating the Impossible, Deepak Malhotra outlines key lessons for negotiating sticky situations, with examples that include the Cuban Missile Crisis, disputes in the National Football League and National Hockey League, and several instances of high-stakes deal-making where companies found themselves negotiating against the odds. Open for comment; 0 Comments.

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Home » Resources » Case Studies » Negotiating with WalMart Buyers

Negotiating with WalMart Buyers

Walmart buyers are trained to treat their vendors in a variety of ways, depending on where you fit into their plan. This case shares a story of a vendor called Sarah who negotiated a win-win outcome with Walmart.

WalMart, the world’s largest retailer, sold $514.4 billion worth of goods in 2019. With its single-minded focus on “EDLP” (everyday low prices) and the power to make or break; suppliers, a partnership with Walmart is either the Holy Grail or the kiss of death, depending on one’s perspective.

There are numerous media accounts of the corporate monolith riding its suppliers into the ground. But what about those who manage to survive, and thrive, while dealing with the classic hardball negotiator?

In “Sarah Talley and Frey Farms Produce: Negotiating with Walmart” and “Tom Muccio: Negotiating the P&G Relationship with Walmart,” HBS professor Jim Sebenius and Research Associate Ellen Knebel show two very different organisations doing just that. The cases are part of a series that involve hard bargaining situations.

“The concept of win-win bargaining is a good and powerful message,” Sebenius says, “but a lot of our students and executives face negotiation counterparts who aren’t interested in playing by those rules. So what happens when you encounter someone with a great deal of power, like Walmart, who is also the ultimate non-negotiable partner?”

The case details how P&G executive Tom Muccio pioneers a new supplier-retailer partnership between P&G and Walmart. Built on proximity (Muccio relocated to Walmart’s turf in Arkansas) and growing trust (both sides eventually eliminated elaborate legal contracts in favor of Letters of Intent), the new relationship focused on establishing a joint vision and problem-solving process, information sharing, and generally moving away from the “lowest common denominator” pricing issues that had defined their interactions previously. From 1987, when Muccio initiated the changes, to 2003, shortly before his retirement, P&G’s sales to Walmart grew from $350 million to $7.8 billion.

“There are obvious differences between P&G and a much smaller entity like Frey Farms,” Sebenius notes. “Walmart could clearly live without Frey Farms, but it’s pretty hard to live without Tide and Pampers.”

Sarah meets Goliath

Sarah Talley was 19 in 1997, when she first began negotiating with Walmart’s buyers for her family farm’s pumpkins and watermelons. Like Muccio, Talley confronted some of the same hardball price challenges, and like Muccio, she acquired a deep understanding of the Walmart culture while finding “new money” in the supply chain through innovative tactics.

For example, Frey Farms used school busses ($1,500 each) instead of tractors ($12,000 each) as a cheaper and faster way to transport melons to the warehouse.

Talley also was skillful at negotiating a coveted co-management supplier agreement with Walmart, showing how Frey Farms could share the responsibility of managing inventory levels and sales and ultimately save customers money while improving their own margins.

“Two sides in this sort of negotiation will always differ on price,” Sebenius observes. “However, if that conflict is the centerpiece of their interaction, then it’s a bad situation. If they’re trying to develop the customer, the relationship, and sales, the price piece will be one of many points, most of which they’re aligned on.”

Research Associate Knebel points out that while Tom Muccio’s approach to Walmart was pioneering for its time, many other companies have since followed P&G’s lead and enjoyed their own versions of success with the mega-retailer. Getting a ground-level view of how two companies achieved those positive outcomes illustrates the story-within-a-story of implementing corporate change.

“Achieving that is where macro concepts, micro imperatives, and managerial skill really come together,” says Sebenius. And the payoffs—as Muccio and Talley discover—are well worth the effort.

Sarah Talley’s Key Negotiation Principles

• When you have a problem, when there’s something you engage in with Walmart that requires agreement so that it becomes a negotiation, the first advice is to think in partnership terms, really focus on a common goal, for example of getting costs out, and ask questions. Don’t make demands or statements. Rather ask if you can do this better. If the relationship with Walmart is truly a partnership, negotiating to resolve differences should focus on long term mutual partnership gains.
• Don’t spend time griping. Be problem solvers instead. Approach Walmart by saying, “Let’s work together and drive costs down and produce it so much cheaper you don’t have to replace me, because if you work with me I could do it better.”
• Learn from and lobby with people and their partners who have credibility, and with people having problems in the field.
• Don’t ignore small issues or let things fester.
• Try not to let Walmart become more than 20% of your company’s business.
• It’s hard to negotiate with well trained buyers who know that their company could put your company out of business.
• Never go into a meeting without a clear negotiation agenda . Make good use of the buyers’ face time. Leave with answers. Don’t make small talk. Get to the point; their time is valuable. Bring underlying issues to the surface. Attack them head on and find resolution face to face.
• Trying to bluff Walmart buyers is never a good idea. There is usually someone willing to do it cheaper to gain the business. You have to treat the relationship as a marriage. Communication and negotiated compromises are key.
• Don’t take for granted that just because the buyer is young they don’t know what they are talking about or that it will be an easy sell. Most young buyers are very ambitious to move up within the company and can be some of the toughest, most educated buyers you will encounter. Know your product all the way from the production standpoint to the end use. Chances are your buyer does, and will expect you to be even more knowledgeable.

My top 3 favorites are don’t ignore small issues, be a problem solver and hold on to a high percentage of your business. You should always communicate when something comes up instead of letting it fester because it could develop into something big that would have never happened if discussed in the first place. When you develop your own business you should never let someone take over more percentage than you have because then you will lose control over what you started. Never gripe and be a problem solver. Larger companies don’t want to hear complaining they want to see action and larger profits

I have negotiated with Walmart for large and small business and I don’t recall any subjects of the conversations that were valued more or equal to price and their margin protection. Logistics or supply it was still a an unyielding stand of profit. Kroger,Publix, Winn Dixie, would &will negotiate for volume -promotions -discounting. Your article is not specific enough for analysis nor to draw the conclusions you present.

The two cases, one with a large vendor and the other with a small one, both working with Wal-Mart reframes some of the classic views of negotiating in a practical way.

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What Is the Negotiation Process? 4 Steps

• 04 May 2023

Negotiation is part of daily life—whether buying a car, leasing property, aiming for higher compensation, raising capital for a startup, or making difficult decisions as an organizational leader.

“Enhancing your negotiation skills has an enormous payoff,” says Harvard Business School Professor Michael Wheeler in the online course Negotiation Mastery . “It allows you to reach agreements that might otherwise slip through your fingers. It allows you to expand the pie [and] create value, so you get more benefits from the agreements that you do reach. It also—in some cases—allows you to resolve small differences before they escalate into big conflicts.”

Here's an overview of the negotiation process’s four steps and how to gain the skills you need to negotiate successfully.

Access your free e-book today.

4 Steps of the Negotiation Process

1. Preparation

Before entering a negotiation, you need to prepare. There are several things to define, including your:

• Zone of possible agreement (ZOPA) : The range in which you and other parties can find common ground. To establish the ZOPA, think about your perspective and your counterpart’s. What do you each want and need? Where might you be willing to compromise?
• Best alternative to a negotiated agreement (BATNA) : Your ideal course of action if an agreement isn’t possible. To determine your BATNA, consider alternatives that provide some of the value you aim to gain from the negotiation. In Negotiation Mastery , Wheeler gives the example that if you can't negotiate down a new car’s price, your BATNA may be to have your old car repaired.
• Walkaway: The line where ending negotiations is better than making a bad deal. Use your BATNA to determine your walkaway. At what point would the BATNA provide more value than a possible negotiated outcome? That’s your walkaway.
• Stretch goal: The best-case scenario for the negotiation’s outcome. It’s critical to give the negotiation a potential ceiling to gauge offers. In Negotiation Mastery, Wheeler recommends choosing a scenario that’s unlikely but not impossible; something that has a 10 percent chance of occurring.

Preparing in advance can improve your confidence, give you clear goals to work toward, and provide a strategy to base your approach on.

2. Bargaining

The second step, bargaining, is what most often comes to mind when thinking about negotiation. Yet, before discussions even begin, there are three levers that determine how the bargaining stage will play out:

• Engaging (the “who”): How do you engage with each other? Is this a friendly conversation, or do you fall into enemy territory?
• Framing (the “what”): How do you define the negotiation? For instance, is it a battle, partnership, or problem to be solved together?
• Norming (the “how”): How do you relate to one another? What behaviors are established that characterize the negotiation?

You typically define these levers in a negotiation’s first few minutes simultaneously. You negotiate the “who,” “what,” and “how” implicitly as the broader negotiation happens explicitly.

How do you and other parties enter the room? Do you greet each other warmly and make small talk, or is there immediate tension? How do you first mention the negotiation? What norms do you imply during the conversation?

Through these levers, you can establish the negotiation’s tone, which is vital as you head into it with someone who may greatly differ from you.

Your counterpart may have different preferences, expectations, risk tolerance, and time horizons. The bargaining stage is about creating value for both you and other parties despite your differences. It requires finding the ZOPA and working within that space to claim the value needed to make the negotiation worthwhile.

“There’s a fundamental tension between creating and claiming value,” Wheeler says in Negotiation Mastery . “Negotiation isn’t one or the other—it’s both at the same time.”

Related: 7 Negotiation Tactics That Actually Work

The third step in the negotiation process is closing—either coming to an agreement or ending the negotiation without reaching one.

How a negotiation closes depends on each party’s walkaway, BATNA, and ZOPA. It also relies on how you use engaging, framing, and norming to create a relationship with the other parties.

If you can’t reach a solution in the ZOPA, perhaps one or more parties decide to go for their BATNA instead. If you and the other parties create and claim value, you may strike a deal.

4. Learning from Your Experience

The final step of the negotiation process is possible to overlook but critical to your ongoing growth: Reflect on your experience. What went well? What went poorly, and why? How do you feel about the outcome?

No two negotiations are the same. The foundational elements can vary (such as the scenarios and people involved), as well as the finer details (for instance, people’s demeanors, emotions , walkaways, and BATNAs).

Reflecting on the process enables you to get to know yourself better as a negotiator and integrate your learnings into your next negotiation.

What Skills Do You Need for Successful Negotiation?

Even after learning about the negotiation process, negotiations can still feel intimidating. To gain confidence, it can help to understand the skills that great negotiators possess .

The best negotiators are strong communicators with high emotional intelligence . Developing your skills in those areas can help you form connections with counterparts and communicate goals. They can also enable you to craft a strategy and remain agile as a negotiation progresses.

“Great negotiators have keen analytical skills,” Wheeler says in Negotiation Mastery . “They assess the matter at hand and craft strategy that best fits those particular circumstances. They know that with negotiation strategy, one size doesn’t fit all.”

Finally, you must create value. As Wheeler puts it in the course: You know how to “expand the pie” rather than argue for a bigger slice—creating value for everyone involved while still achieving your goals.

To learn more about the skills needed for successful negotiation, check out the video below and subscribe to our YouTube channel for more explainer content!

How to Become a Better Negotiator

Familiarizing yourself with the negotiation process and what each step entails can demystify it and help you feel more comfortable.

The best way to improve your negotiation skills is through practice. This can take place in real life through interactions like determining a lease’s terms or asking for your desired salary in job interviews.

If you’d prefer to practice in a supportive learning environment, consider enrolling in an online negotiation course featuring virtual simulations.

In Negotiation Mastery , Wheeler leads you through negotiation practice by pairing you with other learners for mock negotiations. He then debriefs each scenario so you can reflect on it and integrate the insights into future negotiations.

Through thoughtful preparation and dedicated practice, you can strengthen your skills and create value in any negotiation.

Do you want to deepen your understanding of negotiation dynamics? Explore our eight-week online course Negotiation Mastery , one of our online leadership and management certificate programs . Not sure which course is right for you? Download our free flowchart .

About the Author

Cross-disciplinary Challenges: Navigating Power Dynamics in Advocating an Entrepreneurial STEM Curriculum

• Published: 23 May 2024

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• Chun Sing Maxwell Ho   ORCID: orcid.org/0000-0002-1776-3683 1  

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Entrepreneurial STEM, an interdisciplinary approach blending STEM and entrepreneurship education, has become a new trend for cross-subject collaboration that aims to instill an entrepreneurial mindset in students, enabling them to apply their STEM knowledge across various contexts. In this study, we investigate the challenges and corresponding strategies of head science teachers who initiated an entrepreneurial STEM (Science, Technology, Engineering, Mathematics) curriculum in their schools. Grounded in social exchange theory, we explore how head science teachers with entrepreneurial attributes navigated asymmetrical power distribution presented by principals and other subject heads. This collective case study focuses on three schools in Hong Kong that successfully implemented a renowned entrepreneurial STEM curriculum. The findings reveal a common trajectory among head science teachers: initial enthusiastic promotion of the curriculum while meeting resistance; a downscaling and team reform struggles; and a handover and scale-up. This study illuminates the intricate process of balancing power dynamics and stakeholder perceptions through reciprocal negotiation, which were in turn shaped by societal norms.

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Blau, P. (2017). Exchange and power in Social Life . Routledge.

Boraso, R., & Finnigan, K. (2010). Entrepreneurial attitudes and behaviors that can help prepare successful change-agents in Education. The New Educator , 6 (1), 1–29.

Article   Google Scholar  

Chawla, S., & Lenka, U. (2015). A study on learning organizations in Indian higher Educational institutes. Journal of Workplace Learning , 27 (2), 142–161. https://doi.org/10.1108/jwl-07-2014-0052 .

Cialdini, R. B. (2016). Pre-suasion: A revolutionary way to influence and persuade . Simon & Schuster Paperbacks.

Cook, K. S., Cheshire, C., Rice, E. R., & Nakagawa, S. (2013). Social Exchange theory. Handbook of Social Psychology , 61–88. https://doi.org/10.1007/978-94-007-6772-0_3 .

Cropanzano, R., Anthony, E. L., Daniels, S. R., & Hall, A. V. (2017). Social Exchange Theory: A critical review with theoretical remedies. Academy of Management Annals , 11 (1), 479–516. https://doi.org/10.5465/annals.2015.0099 .

Deveci, İ., & Seikkula-Leino, J. (2023). The Link Between Entrepreneurship and STEM Education, Sila Kaya-Capocci, Erin Peters-Burton (Ed.), Enhancing Entrepreneurial Mindsets Through STEM Education (pp. 3–23), Springer.

Deveci, S., & Konuş, F. Z. (2022). The Predictive Power of Turkish Middle School Students’ entrepreneurial competencies on STEM attitudes. The Journal of Entrepreneurship , 31 (2), 425–457. https://doi.org/10.1177/09713557221097178 .

Eltanahy, M., Forawi, S., & Mansour, N. (2020a). Incorporating Entrepreneurial practices into STEM Education: Development of Interdisciplinary E-STEM Model in High School in the United Arab Emirates. Thinking Skills and Creativity , 37 , 100697. https://doi.org/10.1016/j.tsc.2020.100697 .

Eltanahy, M., Forawi, S., & Mansour, N. (2020b). STEM leaders and teachers views of integrating entrepreneurial practices into STEM education in high school in the United Arab Emirates. Entrepreneurship Education , 3 (2), 133–149. https://doi.org/10.1007/s41959-020-00027-3 .

Harris, A. (2008). Distributed leadership: According to the evidence. Journal of Educational Administration , 46 (2), 172–188. https://doi.org/10.1108/09578230810863253 .

Hayat, N., & Amer, I. (2015). Entrepreneurial Orientation- A key to Unlock Teacher’s potential in Higher Education A Case of Finland & Pakistan. Revista Romaneasca Pentru Educatie Multidimensionala , 7 (2), 67–77. https://doi.org/10.18662/rrem/2015.0702.06 .

Hietanen, L., & Ruismäki, H. (2021). Entrepreneurial identity formation through musical identity formation. Music Education Research , 23 (4), 443–453.

Ho, C. S. M. (2023). Unpacking the principal strategies in leveraging weighted student funding. Sustainability, 15 (16), 12592. https://doi.org/10.3390/su151612592

Ho, C. S. M., Bryant, D. A., & Lu, J. (2022). Nurturing teachers’ entrepreneurial behavior in schools: Roles and responsibilities for school principals. Leadership and Policy in Schools, 1 17. https://doi.org/10.1080/15700763.2022.2081218

Ho, C. S. M., & Lee, D. H. L. (2023). The effect of authority transitions on teachers’ entrepreneurial behavior. Teacher Development, 27 (3), 333–352.

Ho, C. S. M., Lu, J., & Bryant, D. A. (2020). The impact of teacher entrepreneurial behaviour: A timelyinvestigation of an emerging phenomenon. Journal of Educational Administration, 58 (6), 697–712. https://doi.org/10.1108/JEA-08-2019-0140

Ho, C. S. M., Lu, J., & Bryant, D. A. (2021). Understanding teacher entrepreneurial behavior in schools: Conceptualization and empirical investigation. Journal of Educational Change, 22 (4), 535–564. https://doi.org/10.1007/s10833-020-09406-y

Ho, C. S. M., & Man, T. W. Y. (2021). The conditions of opportunity recognition in schools: An investigation of how entrepreneurial teachers discover new educational opportunities. Journal of Professional Capital and Community, 7 (2), 109–125. https://doi.org/10.1108/JPCC-04-2021-0022

Hong Kong Education Bureau (2018, August 30). Ongoing renewal of the school curriculum . Education Bureau. https://www.edb.gov.hk/en/curriculum-development/renewal/FAQ.html .

Hyett, N., Kenny, A., & Dickson-Swift, V. (2014). Methodology or method? A critical review of qualitative case study reports. International journal of qualitative studies on health and well-being , 9 (1), 23606.

Joensuu-Salo, S., Peltonen, K., Hämäläinen, M., Oikkonen, E., & Raappana, A. (2020). Entrepreneurial teachers do make a difference – or do they? Industry and Higher Education , 35 (4), 536–546. https://doi.org/10.1177/0950422220983236 .

Kaya-Capocci, S., & Ucar, S. (2023). Entrepreneurial stem for global epidemics. Integrated Science , 467–487. https://doi.org/10.1007/978-3-031-15963-3_25 .

Kidman, G., Gesthuizen, R., Tan, H., & Dielenberg, H. (2023). An entrepreneurial stem teaching framework: Integrating Business and STEM education. Integrated Science , 93–113. https://doi.org/10.1007/978-3-031-17816-0_5 .

Leffler, E. (2020). An entrepreneurial attitude: Implications for teachers’ Leadership skills? Leadership and Policy in Schools , 19 (4), 640–654. https://doi.org/10.1080/15700763.2019.1668021 .

Leithwood, K. (2016). Department-Head Leadership for School Improvement. Leadership and Policy in Schools , 15 (2), 117–140. https://doi.org/10.1080/15700763.2015.1044538 .

Lipscombe, K., Tindall-Ford, S., & Lamanna, J. (2021). School middle leadership: A systematic review. Educational Management Administration & Leadership , 51 (2), 270–288. https://doi.org/10.1177/1741143220983328 .

Martin, J., Cormican, K., Sampaio, S. C., & Wu, Q. (2018). Shared leadership and team performance: An analysis of moderating factors. Procedia Computer Science , 138 , 671–679. https://doi.org/10.1016/j.procs.2018.10.089 .

Martín-Páez, T., Aguilera, D., Perales‐Palacios, F. J., & Vílchez‐González, J. M. (2019). What are we talking about when we talk about STEM education? A review of literature. Science Education , 103 (4), 799–822. https://doi.org/10.1002/sce.21522 .

Merrill, C., & Daugherty, J. (2010). STEM education and leadership: A mathematics and science partnership approach. Journal of Technology Education , 21 (2), 21.

Google Scholar  

National Academy of Sciences (2014). S TEM integration in K-12 education: Status, prospects, and an agenda for research . https://doi.org/10.17226/18612 .

Neneh, B. N. (2019). From entrepreneurial intentions to behavior: The role of anticipated regret and proactivepersonality. Journal of Vocational Behavior, 112 , 311–324.

Peltonen, K. (2015). How can teachers’ entrepreneurial competences be developed? A collaborative learning perspective. Education + Training , 57 (5), 492–511. https://doi.org/10.1108/et-03-2014-0033 .

Rangriz, H. (2012). Organizational climate and ambiguity tolerance with Organizational Entrepreneurship: Empirical study. Journal of Asia Entrepreneurship and Sustainability , 8 (2), 80–113.

Ribeiro, T., Silva, J., Paz, M., Cardoso, A., Teles, N., Nogueira, C., & Ribeiro, T. (2023). Strengthening bridges between STEM education and entrepreneurship: Pathways to societal empowerment towards sustainability. Integrated Science , 25–47. https://doi.org/10.1007/978-3-031-17816-0_2 .

Shane, S. (2012). Reflections on the 2010 AMR Decade Award: Delivering on the Promise of Entrepreneurship as a field of Research. Academy of Management Review , 37 (1), 10–20. https://doi.org/10.5465/amr.2011.0078 .

Shen, H. Z., & Yang, H. (2022). Educational entrepreneurship in Australian community languages schools: An analysis of ethnic principals’ experience and practice. Cogent Education , 9 (1), 1–16.

Spillane, J. P. (2012). Distributed Leadership . Wiley.

Ury, W. (2007). The power of a positive no: How to say no and still get to yes . Bantam.

Wan, Z. H., & Lee, J. C. K. (2017). Hong Kong secondary school students’ attitudes towards science: A study of structural models and gender differences. International Journal of Science Education , 39 (5), 507–527. https://doi.org/10.1080/09500693.2017.1292015 .

Wu, S., & Lin, C. Y. Y. (2019). Educational Innovation, Educational Entrepreneurs and Ecosystem. Innovation and Entrepreneurship in an Educational Ecosystem , 43–53. https://doi.org/10.1007/978-981-32-9445-5_3 .

Zhao, G., Li, G., Jiang, Y., Guo, L., Huang, Y., & Huang, Z. (2022). Teacher Entrepreneurship, Co-creation Strategy, and Medical Student Entrepreneurship for sustainability: Evidence from China. Sustainability , 14 (19), 12711. https://doi.org/10.3390/su141912711 .

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Sample Interview Questions to ETs :

How did you initially become interested in implementing entrepreneurial STEM education in your school, and what factors motivated you to pursue this initiative?

Can you describe the steps you took to introduce and implement entrepreneurial STEM education within your school?

How have power dynamics and social relationships within the school influenced the negotiation process for implementing entrepreneurial STEM education?

Can you share some examples of challenges you faced and negotiations you had with colleagues or principals during the implementation of entrepreneurial STEM education, and how did these negotiations shape the final curriculum and activities?

What strategies did you use to persuade colleagues and principals to support your entrepreneurial STEM education initiatives, especially when faced with conflicting interests or resource constraints?

How have you assessed the impact of entrepreneurial STEM education on both student outcomes and the overall school environment, and what adjustments have you made based on this feedback?

Can you discuss any notable shifts in the perceptions of colleagues, principals, or other stakeholders regarding the value of entrepreneurial STEM education throughout the implementation process?

In what ways have you seen the negotiation dynamics evolve as the entrepreneurial STEM education initiatives progressed in your school?

Have you observed any changes in the social norms or established expectations within your school community as a result of the implementation of entrepreneurial STEM education?

How have your own perceptions of the benefits, costs, and norms associated with entrepreneurial STEM education changed as you have implemented it within your school?

How do you envision the long-term impact of the entrepreneurial STEM education initiative on the beliefs and values of your school community, and how might this affect future educational practices and decision-making?

Sample Interview Questions to Principals and Colleagues :

Can you describe your initial thoughts and feelings when the idea of implementing entrepreneurial STEM education was first introduced in your school? What were your main concerns or reservations?

As the implementation process progressed, what experiences or events contributed to a change in your perspective or attitude towards entrepreneurial STEM education?

How did the communication and collaboration with the teacher in charge of the initiative and other colleagues involved in the project influence your perception of the value of entrepreneurial STEM education?

Can you share any specific examples of how your understanding of entrepreneurial STEM education evolved over time, and what aspects of the initiative were most convincing or influential in changing your mindset?

Were there any particular strategies or approaches used by the teacher in charge or other colleagues that helped you overcome your initial resistance and become more receptive to the idea of entrepreneurial STEM education?

How has your involvement in the project affected your overall teaching philosophy and practices? Have you noticed any changes in your own approach to teaching or classroom management as a result of embracing entrepreneurial STEM education?

In your opinion, what have been the most significant benefits or outcomes of implementing entrepreneurial STEM education within your school? How do these outcomes align with your personal values and beliefs about education?

How have you seen the attitudes of other colleagues, principals, or stakeholders shift throughout the implementation process? Have you observed any notable changes in the school culture or environment as a result of these changing perspectives?

Can you discuss any challenges or obstacles that you faced during the implementation process, and how you were able to overcome them or adapt your perspective to support the entrepreneurial STEM education initiative?

Reflecting on your journey from resistance to acceptance, what advice would you give to other educators who might be skeptical or hesitant about introducing entrepreneurial STEM education in their schools?

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Ho, C.S.M. Cross-disciplinary Challenges: Navigating Power Dynamics in Advocating an Entrepreneurial STEM Curriculum. Res Sci Educ (2024). https://doi.org/10.1007/s11165-024-10172-7

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Your Team Members Aren’t Participating in Meetings. Here’s What to Do.

• Luis Velasquez

Ask yourself: What do people need to feel that their contributions are valued?

Traditional advice for leaders who want to increase meeting participation call for clarifying expectations, setting clear agendas, and asking open-ended questions. While these strategies have their merits, they might not always work because they’re usually based on the leader’s assumptions about what the team needs, rather than facts about what they actually need. Managers who want their teams to be more engaged in meetings need to foster a safe, inclusive team culture, which requires a deep understanding of their team’s unique dynamics. The author presents several strategies for encouraging employees to engage during meetings.

Sue, a former client of mine, was starting a new VP role at a fintech organization. She found out quickly that the team she inherited had a lower level of participation, collaboration, questioning, and general engagement than the one she had left behind. This was particularly evident in team meetings.

• Luis Velasquez , MBA, Ph.D. is an executive coach who works with senior leaders and their teams to become more cohesive, effective, and resilient.  He is the founder and managing partner of  Velas Coaching LLC , a leadership facilitator at the Stanford University Graduate School of Business, a former University professor, and research scientist. Connect with him on  LinkedIn.

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Team-Building Strategies: Building a Winning Team for Your Organization

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• A Top International Negotiation Case Study in Business: The Microsoft-Nokia Deal

International negotiation topics in business: merging two distinct corporate cultures with as little conflict as possible

By PON Staff — on May 2nd, 2024 / International Negotiation

We sometimes require counterparts to meet certain conditions before agreeing to enter into talks. Negotiating conditions to your participation in dealmaking can be a powerful move, but it also carries some risks that need to be carefully considered. And international negotiation brings on more challenges than most. 

Let’s look at the international negotiation case study of Microsoft’s decision to purchase Finnish mobile phone company Nokia’s mobile device business for $9.5 billion. The deal, which closed in 2014, quickly proved disastrous: Microsoft wrote off nearly all of the deal’s value and laid off thousands of workers in July 2015. Although there were many reasons the deal was a bad bet for Microsoft, a negotiating condition that Nokia set before agreeing to take part in serious negotiations may have offered one warning sign. 

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International Negotiation Behind the Microsoft and Nokia Deal: Nokia Builds Its BATNA

Microsoft and Nokia had been partners since 2011, when the Finnish firm began installing Microsoft’s Windows Phone operating system (OS) on its smartphones. But Nokia lagged far behind smartphone competitors in innovation and market share, and the Windows Phone OS, used primarily on Nokia handsets, was failing to meet expectations.

In January 2013, Microsoft CEO Steven Ballmer called Risto Siilasmaa, the chairman of Nokia’s board of directors, to raise the possibility of Microsoft buying divisions of Nokia. Soon after, the two men discussed the idea at a conference in Spain. They agreed inefficiencies existed in their agreement and brainstormed solutions, from minor tweaks to business mergers, reports Ina Fried on the technology news website AllThingsD.com . 

Nokia considered letting its deal with Microsoft lapse and trying to revive its handset business by adapting its smartphones to Google’s Android system. By cultivating this strong BATNA , or best alternative to a negotiated agreement, Nokia gained the power to walk away from a subpar offer from Microsoft.

Indeed, after hearing Microsoft’s first formal pitch for an acquisition in New York, Siilasmaa informed Ballmer that they were too far apart on price and other issues, such as which company would own Here, Nokia’s mapping service. Nokia executives believed they needed to hold on to their ability to sell Here to other companies. Meanwhile, Microsoft felt it couldn’t keep pace with competitors without controlling the mapping technology it was using in its phones, tablets, and PCs, and on the web, according to AllThingsD.com. Subsequent meetings between the parties in London and Finland went nowhere .  

A Deal Takes Shape

A breakthrough came when Nokia informed Microsoft that it would proceed with formal talks only if Microsoft agreed to abide by certain negotiating conditions , most notably a commitment to set up a financing source for Nokia and the caveat that Here was off the table. 

Microsoft agreed. At a meeting in New York, the parties happened upon a solution to the question of who would control the mapping service. Why not share the code, with Nokia retaining intellectual-property rights to Here? Nokia realized it could grant Microsoft a license to access and customize Here’s source code and own any improvements it made. Nokia would retain ownership of Here and the power to license the service to other companies. Ballmer and Siilasmaa shook hands on the outlines of an agreement, which was filled out over the next two months. 

The Risks of Setting Negotiating Conditions

A negotiating condition is an “if” statement—such as, “If you agree to take this issue off the table, I’ll negotiate”—that qualifies your entry into a negotiation or acceptance of a deal. Setting negotiating conditions can be a particularly useful tool when it comes to improving the appeal of another party’s onerous request or demand, notes Harvard Business School and Harvard Law School professor Guhan Subramanian

But insisting that the other party agree to certain terms as a precondition to negotiation can be risky. In their 2012 labor dispute, for example, the musicians of the Minnesota Orchestra said for many months that they would negotiate with the orchestra’s management only after a lockout ended. But management was loath to accept this negotiating condition , aware that the players would have little motivation to accept significant salary cuts if they were performing and being paid. 

Before stipulating a negotiating condition , remember that your counterpart will weigh the costs and benefits of accepting your negotiating conditions against their alternatives away from the table. If you have a strong BATNA , as Nokia appeared to, then it may make sense to take this risk. But note that even in this case, Microsoft made inroads on the mapping service issue that Nokia had claimed was nonnegotiable. Microsoft may have salvaged the deal by refusing to assume that Nokia’s negotiating conditions were nonnegotiable—a move Microsoft’s leaders likely later came to regret.

Two key lessons on negotiating terms and conditions emerge from these failed negotiation examples . First, you should demand only those conditions that are truly deal breakers for you. Second, try to craft negotiating conditions in ways that provide benefits or concessions to your counterpart. Even when you have the power to get what you want, your efforts to help your counterparts get what they want will pay off in the form of stronger relationships and longer-lasting deals.

Have you had experience negotiating conditions to a deal within an international negotiation? If so, how did the process work out?

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No Responses to “A Top International Negotiation Case Study in Business: The Microsoft-Nokia Deal”

3 responses to “a top international negotiation case study in business: the microsoft-nokia deal”.

There are no more phones with ‘Nokia Lumia’. They are all ‘Microsoft Lumia’. Microsoft completely scraped the company and rebranded the devices. Nokia got a bad future

There has been a completely mixed response to whether the deal was good or was a decision taken in a hurry. Nokia surely can use this incoming cash flow on some great products, but the issue now is that Nokia was recognized by its Mobile Devices and there will be almost zero difference between a new product category (coz no more mobile phones)coming under the NOKIA brand name or a completely new Brand name because they will both have zero popularity in that field.

It would probably be good for Nokia to come up with a new brand name and leave the Nokia legacy behind in its Nokia Research Department and nowhere else. As you could feel, this deal saddens me 🙁

It’s 2015 now buddy and Nokia’s all of microsoft now. You should be a lot sad now 😛

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The impact of ozone on Earth-like exoplanet climate dynamics: the case of Proxima Centauri b

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P De Luca, M Braam, T D Komacek, A Hochman, The impact of ozone on Earth-like exoplanet climate dynamics: the case of Proxima Centauri b, Monthly Notices of the Royal Astronomical Society , Volume 531, Issue 1, June 2024, Pages 1471–1482, https://doi.org/10.1093/mnras/stae1199

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The emergence of the JWST and the development of other advanced observatories (e.g. ELTs, LIFE, and HWO) marks a pivotal moment in the quest to characterize the atmospheres of Earth-like exoplanets. Motivated by these advancements, we conduct theoretical explorations of exoplanetary atmospheres, focusing on refining our understanding of planetary climate and habitability. Our study investigates the impact of ozone on the atmosphere of Proxima Centauri b in a synchronous orbit, utilizing coupled climate chemistry model simulations and dynamical systems theory. The latter quantifies compound dynamical metrics in phase space through the inverse of co-persistence ( θ ) and co-dimension ( d ), of which low values correspond to stable atmospheric states. Initially, we scrutinized the influence of ozone on temperature and wind speed. Including interactive ozone [i.e. coupled atmospheric (photo)chemistry] reduces the hemispheric difference in temperature from 68 °K to 64 °K, increases (∼+7 °K) atmospheric temperature at an altitude range of ∼20–50 km, and increases variability in the compound dynamics of temperature and wind speed. Moreover, with interactive ozone, wind speed during highly temporally stable states is weaker than for unstable ones, and ozone transport to the nightside gyres during unstable states is enhanced compared to stable ones (∼+800 DU). We conclude that including interactive ozone significantly influences Earth-like exoplanets' chemistry and climate dynamics. This study establishes a novel pathway for comprehending the influence of photochemical species on the climate dynamics of potentially habitable Earth-like exoplanets. We envisage an extension of this framework to other exoplanets.

The recent discovery of many nearby potentially temperate terrestrial exoplanets provides the opportunity to characterize climates of planets that may be Earth-like (Anglada-Escudé et al. 2016 ; Gillon et al. 2017 ; Rodriguez et al. 2020 ; Delrez et al. 2022 ; Kossakowski et al. 2023 ). Importantly, these temperate planets all have close-in orbits around M-dwarf host stars, which is expected to cause their basic-state climate to be impacted by tidal spin-synchronization (Pierrehumbert & Hammond 2019 ). Most notably, the large day-to-night irradiation contrast is expected to drive strong dayside convection (Yang et al. 2013 ; Sergeev et al. 2020 ) and a planetary-scale Matsuno-Gill pattern of equatorial waves (Showman et al. 2013 ). The combination of dayside convection, potential equatorial super-rotation, and off-equatorial Rossby waves are expected to control the spatial distribution of atmospheric tracers, including clouds (Komacek & Abbot 2019 ; Suissa et al. 2020 ) and photochemically produced chemical species such as ozone (Chen et al. 2021 ; Braam et al. 2023 ).

Ozone (O 3 ) forms from the photolysis of molecular oxygen (O 2 ) via the Chapman mechanism (Chapman 1930 ). On Earth, atmospheric O 2 is produced by photosynthesis and thus an indication of life. Therefore, O 2 and its photochemical by-product ozone have been proposed as potential biosignatures (e.g. Des Marais et al. 2002 ; Schwieterman et al. 2018 ). However, a variety of exoplanet scenarios, including the different ratios of near-UV to far-UV fluxes that planets around M-dwarfs receive, may drive abiotic build-up of O 2 and ozone in planetary atmospheres (e.g. Selsis et al. 2002 ; Domagal-Goldman et al. 2014 ).

Ozone is also a radiatively active species and thus impacts a planetary atmosphere's thermal and dynamic structure. Being both (photo)chemically and radiatively active makes ozone one of many potential species that induce climate-chemistry interactions, which have received considerable attention in models of the Earth System (e.g. Ramanathan et al. 1987 ; Isaksen et al. 2009 ), also as part of the Inter-governmental Panel on Climate Change reports (IPCC 2021 ). The radiative impact of ozone consists of two components. First, the stratospheric ozone layer absorbs incoming UV radiation on Earth. This layer protects the surface from harmful UV fluxes, which is also the case when considering the radiation received by exoplanets around M, K, G, and F-type stars (e.g. Segura et al. 2003 , 2005 ) or the 3D impact of stellar flares from M-dwarfs (Ridgway et al. 2023 ). Ozone then emits thermal energy at infrared wavelengths, heating the stratosphere and producing a temperature inversion, which is also predicted for various exoplanets (e.g. Godolt et al. 2015 ). Secondly, ozone in the upper troposphere acts as a greenhouse gas, absorbing the outgoing radiation from a planet. The radiative effect of ozone strongly depends on the 3D (vertical and horizontal) distribution through the atmosphere, which is ultimately determined by the complex interplay between (photo)chemistry and atmospheric dynamics. Studying such climate-chemistry interactions motivates using a 3D coupled climate-chemistry model (CCM).

A growing body of work uses CCM simulations to study Earth-like exoplanets in a synchronized orbit. Generally, significant hemispheric contrasts in ozone exist for planets around M-dwarfs (e.g. Chen et al. 2018 ; Yates et al. 2020 ), and such spatial variations should affect future observations (Cooke et al. 2023 ). Simulations of Proxima Centauri b predict a significant zonal structure in the ozone distribution with accumulation of ozone at the gyre locations (Yates et al. 2020 ), driven by a stratospheric circulation connecting the photochemically active dayside and the gyres on the nightside (Braam et al. 2023 ). Furthermore, Yates et al. ( 2020 ) have shown that steady-state climate conditions differ when ozone is computed interactively, depending on photochemistry, atmospheric circulation, and temperature, compared to the simulations without ozone and with a fixed Earth-like ozone profile (Boutle et al. 2017 ). However, simulations of Proxima Centauri b also show different versions of internal variability in, for example, stratospheric winds (Cohen et al. 2022 ) and planetary-scale waves (Cohen et al. 2023 ), affecting the climate and distributions of atmospheric tracers. At present, a full assessment of the impact of ozone on key atmospheric variables and climate dynamics by also applying a novel dynamical systems theory approach is the logical next step (De Luca et al. 2020a , 2020b ; Faranda et al. 2020 ).

Dynamical systems theory is the discipline that studies the trajectory of a given chaotic dynamical system, such as an atmosphere, by analysing Poincaré recurrences in phase space. Recent developments have seen Poincaré recurrences combined with extreme value theory (Lucarini et al. 2012 ; Faranda et al. 2017 ). This approach allows us to quantify two main metrics, the inverse of local persistence ( θ ) and local dimension ( d ), which are instantaneous in time and computed for 2D latitude-longitude maps. The former indicates the mean residence time of a given number of states around a state of interest. The latter provides information about the active degrees of freedom of the same states in the atmospheric phase space. The lower the θ and d , the more stable (in the sense of atmospheric variability) the atmospheric motion of the variable of interest, whereas the higher the θ and d , the less stable the trajectory of the atmospheric variable. The methodology has been used for univariate atmospheric variables such as temperature, precipitation, and geopotential height, and various studies proved its usefulness in analysing the climate dynamics of Earth (e.g. Hochman et al. 2019 , 2020 ; Vakrat & Hochman, 2023 ; Wedler et al. 2023 ) and terrestrial exoplanets (Hochman et al. 2022 , 2023 ). The method has also more recently been expanded to assess two (or more) atmospheric variables simultaneously (De Luca et al. 2020a , 2020b ; Faranda et al. 2020 ). Moreover, in this compound case, one can obtain two dynamical metrics: the inverse of local co-persistence ( θ T,WS ) and local co-dimension ( d T,WS ). They resemble the univariate metrics, with the only difference being that they are computed from two atmospheric variables of interest, temperature (T) and wind speed (WS), in two different phase spaces. Therefore, their values are obtained from joint recurrences, and we define them here as compound dynamical metrics.

Our main aim is to leverage climate model simulations of Proxima Centauri b, traditional atmospheric analysis, and dynamical systems theory to understand how ozone influences key atmospheric variables and climate dynamics. Section 2 describes the climate model setup and data, the computation of the compound dynamical systems metrics, and statistical inference. In Section 3 , we present our results regarding the direct effects of ozone on atmospheric variables and dynamics. We discuss our findings for Proxima Centauri b and provide conclusions extended to the broad range of Earth-like exoplanets in Section 4 .

2.1 Coupled climate-chemistry model

We use a 3D coupled Climate-Chemistry Model (CCM) consisting of the Met Office Unified Model (UM) and the UK Chemistry and Aerosol framework (UKCA). Braam et al. ( 2022 ) described the CCM in extensive detail. Here, we limit ourselves to a brief description of the essential components relevant to this study. A 3D CCM simulates the coupled evolution of radiative transfer, dynamics, and chemistry in a planetary atmosphere, comprehensively assessing the planetary climate and habitability.

The UM is a versatile General Circulation Model, using the ENDGame dynamical core to solve the equations of motion (Wood et al. 2014 ) and the Suite of Community Radiative Transfer codes based on the Edwards and Slingo scheme to compute radiative transfer (SOCRATES; Edwards & Slingo 1996 ). The incoming stellar radiation from Proxima Centauri (M5.5 V star) is based on the v2.2 composite spectrum from the MUSCLES spectral survey (France et al. 2016 ; P. Loyd et al. 2016 ; Youngblood et al. 2016 ). Sub-grid scale processes like convection (Gregory & Rowntree, 1990 ), water cloud physics (Wilson et al. 2008 ), and turbulent mixing (Lock et al. 2000 ; Brown et al. 2008 ) are parametrized. Besides the common use of the UM in predicting the Earth's weather and climate, it has been adapted to Mars (McCulloch et al. 2023 ) and exoplanets ranging from terrestrial planets (e.g. Mayne, Baraffe, Acreman, Smith, Wood, et al. 2014 ; Boutle et al. 2017 ) to hot Jupiters (e.g. Mayne, Baraffe, Acreman, Smith, Browning, et al. 2014 ; Amundsen et al. 2016 ).

UKCA is a framework to simulate 3D kinetic and photochemistry (Morgenstern et al. 2009 ; O'Connor et al. 2014 ; Archibald et al. 2020 ; Braam et al. 2022 ). The atmospheric transport of chemical tracers is fully coupled to the UM's large-scale advection, convection, and boundary layer mixing. Here, we limit ourselves to UKCA's gas-phase (photo)chemistry description. The chemical network consists of 21 chemical species connected by 71 reactions (as shown in the appendix of Braam et al. 2022 ). The network describes the Chapman mechanism of ozone formation as well as the catalytic destruction of ozone by the hydrogen oxide and nitrogen oxide catalytic cycles, representing interactive ozone chemistry in the 3D model.

We simulate Proxima Centauri b (Anglada-Escudé et al. 2016 ) as an aqua planet orbiting in a 1:1 spin-orbit resonance around its M-type host star, using the orbital parameters described in Table  1 . Anglada-Escudé et al. ( 2016 ) well-constrained the semimajor axis and orbital period. Given the close-in orbit at 0.0485 AU, a 1:1 spin-orbit resonance or synchronous orbit is a probable scenario (Barnes 2017 ) and results in a rotation rate of 6.501 × 10 −6  rad s −1 . The stellar irradiance follows from Boutle et al. ( 2017 ). Since Proxima Centauri b is non-transiting, we only have a lower limit on its mass from the detection by the radial velocity method of M p sin (i)  = |$1.07\ \pm \ 0.06$| M ⨁ (Anglada-Escudé et al. 2016 ; Faria et al. 2022 ), where i is the orbital inclination. Given the unknown actual mass of Proxima Centauri b and to ensure consistency with previous GCM simulations, we follow Turbet et al. ( 2016 ) and assume an actual planet mass of 1.4 M ⨁ . Assuming that Proxima Centauri b has Earth's density (5.5 g cm −3 ), we estimate a corresponding planetary radius of 1.1 R ⨁ and a surface gravity of 10.9 m s −2 . While these configurations are based on the known parameters of Proxima Centauri b, the simulation results can apply more generally to planets with similar sizes and rotation periods in spin-synchronous orbits around M-dwarf stars. We use a horizontal resolution of 2° × 2.5° in latitude and longitude, respectively, with the substellar point at 0° latitude and longitude. We assume the entire surface is covered by a 2.4 m slab ocean mixed layer with a total heat capacity of 10 7  J K −1 m −2 . We simulate an atmosphere extending up to 85 km altitude, divided over 60 vertical levels that are quadratically stretched for enhanced near-surface resolution (Yates et al. 2020 ). Abundances of N 2 , O 2 , and CO 2 (Table  1 ) correspond to pre-industrial Earth levels, and water vapour profiles are determined interactively following evaporation from the slab ocean.

Orbital, planetary, and atmospheric parameters used to configure Proxima Centauri b following Boutle et al. ( 2017 ). Note that the mass fractions of H 2 O and O 3 are interactively calculated; therefore, they are given as a range indicating minimum and maximum values. H 2 O follows from the balance of evaporation, condensation, (photo)chemistry, and O 3 from (photo)chemistry.

We initialize the No-Chemistry setup with the uniform mass mixing ratios of N 2 , CO 2 , and H 2 O from surface evaporation. CO 2 and H 2 O, as radiatively active species, are important factors in the thermodynamic and dynamic state of the atmosphere. For the Chemistry simulation, we also specified a uniform mass mixing ratio for O 2 and included the interactive calculation of ozone chemistry. Ozone is another radiatively active species, and its interactively determined and varying mixing ratios are used in the radiative transfer calculations, potentially affecting the thermodynamic and dynamic state of the atmosphere. We spin up both simulations for ∼20 Earth years to ensure a steady state, diagnosed by radiative balance, surface temperatures, and ozone abundances. After that, we run the simulations for another 30 yr with daily output to analyse Proxima Centauri b's atmospheric dynamics.

We extract two atmospheric variables from the 30-yr Chemistry and No-Chemistry simulations: temperature (T in °K), linked with thermodynamic processes, and wind speed (WS in m s −1 ), related to dynamic processes. In addition, we obtain the vertically integrated ozone column density in DU (1 DU = 2.69 × 10 20 molecules m −2 ) and ozone mass fraction (kg kg −1 ) over the same levels, hereafter OzCol and OzFr, respectively. From these four variables, we use all 60 vertical levels when assessing their vertical profiles and choose one level for computing composite and difference maps. This level corresponds to ∼22 km for T, WS, and OzFr since we find the largest concentration of ozone particles at this level. For OzCol, we use the surface level representing the vertically integrated amount of overhead ozone molecules in the vertical column. We then provide vertical profiles for these four atmospheric variables and compute them for the global, northern, and southern gyre regions. For each variable, simulation, and atmospheric vertical level, we take the temporal median over the entire 30-yr period and then compute the field median. This leaves us with 60 data points for each variable and region representing the atmosphere.

2.2 Dynamical systems metrics

We used a novel dynamical systems method to compute two compound dynamical metrics: the inverse of local co-persistence and local co-dimension, which we refer to as θ T,WS , and d T,WS , respectively. The metric θ T,WS is intuitively a measure of the joint average residence time of two trajectories around two respective states of interest. The lower the value of θ T,WS , the more likely it is that the preceding and future states of the systems will resemble the current states. The metric d T,WS describes the joint evolution of the systems around two respective states of interest and can be interpreted as a proxy for the joint number of degrees of freedom active around the same states (De Luca et al. 2020a , 2020b ; Faranda et al. 2020 ).

Calculating the compound dynamical systems metrics combines Poincaré recurrences with extreme value theory (Freitas et al. 2010 ; Lucarini et al. 2012 ; Faranda et al. 2017 , 2020 ). We referred to the system returning n times close to a previously visited state in the phase space as recurrences . We considered an atmospheric variable, such as T, and a given state of interest, namely a 2D map of a day within the time series of T. Our approach uses the Euclidean distance to quantify how close the state of interest and the recurrences are to one another in the atmospheric phase space (Faranda et al. 2017 ).

We considered a second phase space for the latter variable to extend the dynamical systems analysis to two variables, T and WS. Eventually, we computed joint recurrences around a common state of interest, corresponding to two instantaneous latitude–longitude maps: one for T and one for WS. Once we defined the joint recurrences, we computed θ T,WS , and d T,WS compound metrics for the 60 vertical levels in the Proxima Centauri b's climate model simulations. The final output of such analysis is a value for each metric, daily time-step, and vertical level. This allows us to relate specific metric values to the corresponding geographical patterns of selected atmospheric variables. We further computed the compound dynamical metrics for particular regions of interest: the northern gyre, where atmospheric ozone tends to accumulate, and equatorial western and eastern terminators, which are highly variable (Fig.  1e ). Finally, we defined ‘High’ and ‘Low’ dynamically stable days as the lower and upper 5 per cent of θ T,WS , and d T,WS compound metrics, respectively. For a complete derivation of θ T,WS , and d T,WS we refer the reader to Faranda et al. ( 2020 ).

Climatology for key variables in the Chemistry and No-chemistry model simulations. (a–b) Temperature (T in °K). (c–d) Wind speed (WS in m s −1 ). (e) Ozone column density (OzCol in DU). (f) Ozone fraction (OzFr in kg kg −1 ). Median composites were computed over the 30 yr for Chemistry (a, c, e, f) and No-Chemistry (b, d) simulations. Climatology of (a-d, f) was computed from the ∼22 km level, whereas for (e) from the surface level. In (e) we mark the geographical regions used with rectangles: northern gyre (Lon 146.25°, -93.25°, Lat 39°, 83°); southern gyre (Lon 146.25°, -93.25°, Lat -39°, -83°); equatorial western terminator (Lon -105°, -75°, Lat -15°, 15°); and equatorial eastern terminator (Lon 75°, 105°, Lat -15°, 15°).

2.3 Statistical inference

We perform a two-tailed Wilcoxon rank-sum test to assess the statistical significance of the median vertical profiles and difference maps (Mann & Whitney, 1947 ). The test was performed between the Chemistry and No-Chemistry medians, composite data sets, and between compound stable and unstable atmospheric states under the null hypothesis that the medians of the data sets are equal. We then compute the composite maps' corresponding p -values at the grid-point level. To account for Type I errors (or false positives), we apply the Bonferroni correction of p -values (Bonferroni, 1936 ), which divides the original p -values by the total number of statistical tests performed. Lastly, to assess the statistical significance of the standard deviation's vertical profiles, we perform the F-test under the null hypothesis that the variances of the two populations are equal (Snedecor & Cochran, 1989 ). We provide all statistical tests at the 1 percent significance level.

3.1 How does interactive ozone influence the climatology of atmospheric variables?

Fig.  1 shows the 30-yr climatology of four atmospheric variables, i.e. T, WS, OzCol, and OzFr, for both Chemistry and No-Chemistry simulations. We note that the stratospheric temperature for the Proxima Centauri b Chemistry simulation increases globally compared to the No-Chemistry due to the different chemical compositions (Figs.  1a and  b ). The ozone layer (Fig.  1e ) and particularly stratospheric ozone (Fig.  1f ) in the Chemistry simulation absorbs incoming ultraviolet radiation and reemits this at infrared wavelengths, leading to warming in the stratosphere. On the other hand, the temperature gradient between the two simulations is kept, meaning that T at higher (northern and southern) latitudes reaches its minimum and gradually increases meridionally towards the equatorial region (Figs.  1a and  b ). The wind speed shows a similar spatial distribution for the Chemistry and No-Chemistry climatology (Figs.  1c and  d ), with lower wind speed at higher latitudes and an increase towards the equatorial jet. Nevertheless, the jet's intensity changes with weaker eastward winds at the equator for the Chemistry simulation. Taking the surface temperature as a proxy for day-to-night contrasts, we determine a hemispheric contrast (dayside average minus nightside average) of 64 °K and 68 °K for the Chemistry and No-Chemistry climatology, respectively. The smaller day-to-night temperature contrast for the Chemistry climatology may be the reason for a weaker jet considering thermal wind balance. Lastly, both ozone climatologies show similar patterns with the higher concentration of ozone in the northern and southern gyre regions (Figs.  1e and  f ). In contrast, for OzFr, we still observe higher ozone values in the proximity of the gyres and across the mid and higher latitudes with a meridional gradient of lower values towards the equator (Fig.  1f ). The difference between OzCol and OzFr climatology is due to the former representing ozone integrated over the entire vertical column, whereas the latter is strictly confined to stratospheric ozone fraction. Spatial variations in the distribution of ozone are driven by stratospheric circulation mechanisms, including an analogue of the Brewer-Dobson circulation that controls the ozone distribution on Earth and the stratospheric dayside-to-nightside circulation for synchronously rotating planets (Braam et al. 2023 ).

The temperature vertical profiles look similar between the global and gyre regions (Figs.  2a–c ). However, both gyres exhibit lower temperatures (∼175 °K) than the global median (∼211 °K) at the surface. Such a temperature difference is noticeable within the first 5–6 km from the surface because these gyres trap air, subject to extensive radiative cooling due to the nightside location. For both Chemistry and No-Chemistry and all three regions, we observe an increase in temperature, then an inversion, and a slight increase up to the top of the atmosphere. A significant difference is that the temperature for the Chemistry simulation is significantly higher (∼+7 °K) than the No-Chemistry one from ∼17 km to ∼50 km in all three regions, probably because at this altitude range, we find the highest ozone mass fraction (Figs.  2j–l ). The vertical profiles for wind speed are also very similar between all the regions in the Chemistry and No-Chemistry simulations (Figs.  2d–f ). However, the wind speed in the Chemistry simulation in the gyres is significantly higher (∼+5 m s −1 ) than the No-Chemistry one. This may be due to multiple complex factors since the location of the gyres and strength of the rotating winds will depend on the radiative forcing and heat transport (e.g. Showman et al. 2013 ; Pierrehumbert & Hammond 2019 ), which slightly change due to the inclusion of ozone. The values of OzCol are higher from ∼0 to ∼20 km over the gyres compared to the global region (Figs.  2g–i ; Braam et al. 2023 ). The OzCol = 0 DU from ∼40 km upwards for all three regions. However, OzFr in all three regions increases from the surface to ∼48 km when it reaches its maximum and then decreases close to 1e -08  kg kg −1 at ∼76 km (Figs.  2j–l ). Between the global and the gyre profiles, we notice a difference close to the peak in OzFr: the vertical distribution of ozone over the gyre regions shows a saddle from ∼48 to ∼60 km due to the formation of a secondary ozone layer on the nightside hemisphere in the absence of ozone photolysis (e.g. Smith & Marsh 2005 ).

Vertical profiles of four atmospheric variables. (a–c) Temperature – T, (d–f) Wind speed – WS, (g–i) Ozone column – OzCol and (j–l) Ozone fraction – OzFr. The first column represents vertical profiles computed from global medians over the 30 yr. In contrast, the second and third columns represent the same, but for the northern and southern gyres, where the concentration of ozone is higher. (a–f) Profiles of the Chemistry and No-Chemistry simulations. (g–l) Profiles computed from the Chemistry simulation. Circles in (a–f) represent Chemistry and No-chemistry medians that are not significantly different at the 1 percent level. OzFr in (j–l) is plotted on a log 10 scale.

3.2 How does interactive ozone influence the atmospheric dynamics?

Here, we analyse the influence that interactive ozone has on the dynamics of Proxima Centauri b's atmosphere. In this respect, we show the median vertical profiles of the compound dynamical systems metrics (Fig.  3 ). Globally, although relatively small, we find significant differences between the Chemistry and No-Chemistry simulations. A substantial decrease in θ T,WS , and d T,WS is observed below the levels of maximum OzFr and an increase above these levels (compare Figs.  3a , e with Fig.  2j ). Some levels, especially for d T,WS , do not show significant differences. These findings are also apparent in the north gyre (Figs.  3b , f ) and west and east terminators (Figs  3c–d , g–h ). However, for the terminators, we note that Chemistry's and No-Chemistry's co-dimension shows lower values over the entire vertical profile when compared to the global and north gyre regions. We further display the standard deviations vertical profiles of θ T,WS , and d T,WS (Figs.  3i–p ). We provide evidence for significantly larger variability in the atmospheric time series dynamics of Proxima Centauri b when including interactive ozone than not having it. This finding is particularly evident just below the level of maximum ozone accumulation.

Vertical profiles of compound dynamical systems metrics. (a–d) The inverse of local co-persistence ( θ T,WS ). (e–h) Local co-dimension ( d T,WS ) medians for Chemistry and No-Chemistry simulations. (i–p) the same but for the standard deviations. The first column shows the global vertical level values over the 30 yr, the same for the second column but for the northern gyre. The third and fourth columns are for the western and eastern equatorial terminators. The dynamical system metrics are computed from temperature (T) and Wind Speed (WS). Circles represent (a–h) medians and (i–p) standard deviations that are not significantly different at the 1 percent level.

Next, we selected ‘High’ (upper 5 percent) and ‘Low’ (lower 5 percent) θ T,WS , and d T,WS days in the Chemistry and No-Chemistry simulations (Fig.  4 ). Joint low values reflect more stable (in the sense of atmospheric time series variability) atmospheric states, whereas joint higher values are relatively unstable atmospheric configurations. Also, from Fig.  4 , it is possible to notice an increased variability for the Chemistry simulation compared to the No-Chemistry since the data points in the former tend to spread more over the x and y axis compared to the latter.

Scatter plots of θ T,WS (x-axis) and d T,WS (y-axis) for (a) Chemistry and (b) No-Chemistry simulations. The compound dynamical systems metrics are computed from temperature and wind speed at the ∼22 km level. Bottom left and top right shaded areas contain states with θ T,WS and d T,WS  < 5th and > 95th percentiles, ‘Low’ and ‘High’, respectively. On the top left of each panel, we show the Spearman's correlation coefficient and p -value.

We calculate field medians or composite maps for the ‘High’ and ‘Low’ atmospheric states from Fig.  4 . Next, we analysed the differences between the median composite maps of temperature and wind speed for ‘High’ and ‘Low’ atmospheric states in the Chemistry and No-chemistry simulations at the vertical level corresponding to ∼22 km altitude (Figs.  5 and 6 ). Fig.  5 shows the composite and difference maps for temperature. Here, the Chemistry simulation has higher temperatures in both ‘High’ and ‘Low’ states than the No-Chemistry simulation, thanks to the large abundance of OzFr at this level leading to radiative heating. In addition, temperature patterns are symmetrical between the northern and southern regions of Proxima Centauri b, with lower values at higher latitudes and higher values across the tropical region (Figs.  5a–d ). Difference maps of High–Low states point towards enhanced temperatures for the ‘High’ states over the planet, with both Chemistry and No-Chemistry simulations also showing slightly higher values in the gyre regions (up to + 6 °K). This pattern is more pronounced in the former simulation (Figs.  5e–f ), and this is due to a higher accumulation of ozone in the ‘High’ states compared to ‘Low’ ones. Difference maps for Chemistry–No-Chemistry shows positive and significant temperature differences over the entire planet for both ‘High’ and ‘Low’ states (up to +15  °K) again due to ozone's radiative heating. Nevertheless, we note that ‘High’ states' positive temperature differences are observed over the mid-latitudes, whereas the ‘Low’ states positive temperature differences occur over the tropics (Figs.  5g–h ).

Composite and difference maps for temperature (T) at the ∼22 km level. (a–b) Composite maps are field medians computed from Chemistry and No-Chemistry joint co-persistence and co-dimension states (defined in Fig.  4 ), which are > 95th percentile – ‘High,’ and (c–d) the same but for states < 5th percentile – ‘Low.’ (e–f) Difference maps were computed by subtracting the ‘Low’ from the ‘High’ composites for Chemistry and No-Chemistry simulations. (g–h) Difference maps were calculated by subtracting the No-Chemistry from the Chemistry composites for both ‘High’ and ‘Low’ states. In (e–h), stippling represents areas that are not significantly different at the 1 percent level.

Same as Fig.  5 but for Wind Speed (WS).

Composite maps for wind speed show very similar and symmetrical patterns of high wind speed over the tropics (corresponding to the equatorial jet) and lower wind speed in the higher latitudes, with the only difference being the Chemistry ‘Low’ states simulation that has weaker wind speed values in the tropics (Figs.  6a–d ). This shows that the addition of interactive ozone substantially affects the persistent atmospheric states by weakening the equatorial jet (Fig.  6c ). This may imply that the mechanism that drives the equatorial jet on synchronously rotating exoplanets (Showman et al. 2013 ) diminishes in strength with the inclusion of ozone. This causes less pronounced gyres, which we will show with the composite maps of the OzCol below. In Section 4 , we will put these findings on the equatorial jet and gyres into the context of the large-scale atmospheric circulation. Difference maps between High–Low show positive and high wind speed differences (up to +35 m s −1 ) from ∼50 |$^\circ $| S to ∼50 |$^\circ $| N, with higher values for the Chemistry simulation than the No-Chemistry one. In the Chemistry simulation, we also provide evidence for negative wind speed differences (up to −10  m s −1 ) over the gyres (Figs.  6e–f ). Difference maps for Chemistry–No-Chemistry ‘High’ states show positive wind speed values (up to +15 m s −1 ) over most of the planet and negative differences in the gyres (up to −5  m s −1 ). The same maps for ‘Low’ states show stronger negative wind speed differences (up to −25  m s −1 ) from ∼50 |$^\circ $| S to ∼50 |$^\circ $| N, and weak positive differences for most of the remaining planet (Figs.  6g and  h ).

Similar to temperature and wind speed, we also computed the composite and difference maps for OzCol and OzFr, with the only difference being that here, we only use the Chemistry simulation. When looking at the Chemistry composite maps of both OzCol and OzFr during ‘High’ and ‘Low’ atmospheric states, we observe that higher states lead to higher accumulation of ozone over both the northern and southern gyres (Figs.  7a–b , d–e ), driven by a stratospheric dayside-to-nightside circulation (Braam et al. 2023 ). However, for OzFr, higher values of ozone are also found from 50 |$^\circ $| S to 90 |$^\circ $| S and from 50 |$^\circ $| N to 90 |$^\circ $| N, caused by the combined effect of atmospheric circulation and weaker chemical loss processes of ozone the further we move from the substellar point (Fig.  7d ) (e.g. Chen et al. 2018 ; Yates et al. 2020 ). Such spatial patterns are, therefore, reflected when looking at the difference maps of High–Low states. Indeed, we find positive differences for the ‘High’ states of OzCol over the northern and southern gyres, and the same is true for OzFr, but with more prominent enhanced values at higher latitudes. Moreover, the former variable shows negative differences over most of the remaining planet, and the latter shows negative and non-significant differences from ∼10 |$^\circ $| S to ∼10 |$^\circ $| N (Figs.  7c and  f ). Hence, the composite maps of temperature, wind speed, and ozone together illustrate that the stratospheric dayside-to-nightside circulation that drives ozone accumulation over the gyres is most prevalent during the ‘High’ states. On the other hand, the ‘Low’ states represent a relatively weak dayside-to-nightside circulation, illustrated by less pronounced gyres and a more homogeneous ozone distribution.

Same as Fig.  5 but for OzCol (a–c) and OzFr (d–f). Note that the figure shows the Chemistry simulation. In (c, f), stippling represents areas that are not significantly different at the 1 percent level.

The atmospheres of tidally locked terrestrial (or Earth-like) exoplanets are close to being characterized by the advent of the JWST . This opens new frontiers in searching for habitable planets outside our solar system and incentivizes new ground-breaking investigations from the astrophysical, astronomical, and Earth sciences communities. With this work, we showed that adding an interactive ozone module to climate model simulations of Proxima Centauri b globally increases the stratospheric temperature and induces regionally varying effects on the surface temperature, including increased surface temperature in the gyre regions and a decrease of the dayside-to-nightside temperature contrast by 4  |${}^\circ $| K. Adding ozone in the simulations resulted in similar albeit significantly different median vertical compound dynamics of temperature and wind speed compared to not having interactive ozone, with more differences observed when assessing their standard deviations, indicating enhanced variability. We found that highly dynamically stable states have warmer gyre regions, stronger wind speeds, and enhanced ozone accumulation in the gyres.

Our findings can be summarized and contextualized as follows:

Chemistry model simulations show higher average stratospheric temperatures compared to No-Chemistry ones. We attribute this difference to the ozone's radiative heating, a similar mechanism that we observe in the Earth's stratosphere due to the absorption and emission of terrestrial IR radiation and absorption of solar radiation in the UV and visible spectrums (Dopplick, 1972 ; Park & London 1974 ; Fishman et al. 1979 ). The temperature difference was in the order of + 7 |${}^\circ $| K and can be observed from ∼17 to ∼50 km above the surface. The altitude range where the highest ozone mass fractions are found and where ozone is most likely to interact with the incoming stellar radiation. This agrees qualitatively with previous studies on the effect of ozone on vertical temperature structures, with Boutle et al. ( 2017 ) also reporting warming of the stratosphere for Proxima Centauri b. However, the quantitative warming effect of ozone varies. Godolt et al. ( 2015 ) have shown that ozone heats the stratosphere of planets around F-type stars but does not significantly affect the vertical temperature structure of planets around K-type stars. The spectral dependence is further illustrated by Kozakis et al. ( 2022 ), showing that ozone abundances and the amount of stratospheric heating depend on the total amount of UV flux received from the host star and the distribution over wavelengths. The amount of incoming near-ultraviolet (NUV: 200<λ<400 nm) radiation determines ozone production, while the far-ultraviolet (FUV: 91<λ<200 nm) radiation determines the amount of oxygen photolysis and, thus, ozone production. Hence, the total UV flux and the FUV/NUV flux ratio are important metrics of ozone photochemistry and its impact on climate dynamics. Even if we only consider the photolysis wavelengths in UM-UKCA (λ>177 nm), the MUSCLES spectrum used in this study had an FUV/NUV flux ratio of 0.012, a higher ratio than any of the host stars from Kozakis et al. ( 2022 ) and sufficient to drive mild stratospheric heating. The altitude that corresponds to the stratospheric ozone layer and its effect on the vertical temperature structure depends on the initial amount of O 2 present (Cooke et al. 2022 , 2023 ).

The gyres of Proxima Centauri b show a ‘saddle’ in the OzFr vertical profile, which the global ones do not. Since the nightside is devoid of incoming radiation, the balance of ozone formation (three-body reaction O + O 2  + M → O 3  + M) and ozone destruction (driven by photolysis and reaction with atomic O) in the Chapman mechanism shifts to more ozone production. This leads to a secondary nightside ozone layer at high altitudes. A mesospheric secondary ozone layer is also present during night-time on Earth (e.g. Smith & Marsh 2005 ). Its permanent presence on the nightside of synchronously rotating planets was also found in simulations of Earth in a synchronous orbit (Proedrou & Hocke 2016 ).

Adding interactive ozone to the simulations affects the compound dynamics of temperature and wind speed. Both Chemistry and No-Chemistry simulations showed similar patterns of θ T, WS , and d T, WS vertical profiles when taking the medians over the 30 yr in the entire planet, northern gyre, and western and eastern terminators. However, most of the vertical profiles showed statistically significant differences. We noticed more variability for the Chemistry simulation than the No-Chemistry one when considering the standard deviations. We therefore suggest that including interactive ozone improves the simulation of Proxima Centauri b's atmospheric time series dynamics, since increased variability broadly means a more realistic simulation of the atmospheric dynamics. Ozone, as a single interactive species, can significantly impact the compound dynamical metrics on both global and regional scales, depending on the stellar flux distribution and the initial oxygen content. From Fig. 7 of Kozakis et al. ( 2022 ), ozone heats the atmosphere more for planets orbiting earlier stellar types. This relates to the FUV/NUV ratio, but perhaps even more so simply to the magnitude of the UV radiation, as shown in their Fig. 2.

Highly dynamically stable states show larger ozone column and fraction over the gyres than ‘Low’ states. ‘Low’ states reflect stalling (or more persistent) weather patterns compared to the more variable ‘High’ states. The Chemistry simulation showed a significant increase in OzCol in ‘High’ states over the northern and southern gyres’ regions on the nightside, along with increased OzFr. On synchronously rotating planets, the day-nightside heating contrast generates an overturning circulation with rising air on the dayside and subsiding air on the nightside (Showman et al. 2013 ; Hammond & Lewis, 2021 ). The overturning circulation has a strong tropospheric component but extends into the stratosphere, with implications for photochemically generated ozone at these altitudes (Braam et al. 2023 ). These vertical motions, in turn, contribute to forming standing, planetary-scale Kelvin and Rossby waves, the latter of which manifest as the nightside gyres in our simulations (Showman et al. 2013 ). Photochemistry is not active in these non-irradiated gyre regions, and the enhanced OzCol is regulated by the stratospheric overturning circulation (Braam et al. 2023 ). This picture implies that the large-scale circulation, atmospheric variability, and OzCol variations are linked. We postulate that ‘High’ θ T, WS , and d T, WS states may represent migration in time for the gyres (see also Cohen et al. 2023 ), oscillating in their central longitude so that naturally, these states show enhanced variability. Furthermore, we postulate that these ‘High’ states have a particularly strong overturning circulation, enhancing the amount of ozone trapped in the gyres.

Wind speed for Chemistry ‘Low’ states is much lower than for ‘High’ states.

The existence of the gyres is related to the mechanism to form equatorial super-rotating jets on synchronous exoplanets since the planetary-scale waves (including the Rossby waves, which the gyres are lows of) pump eastward momentum equator-wards (Showman & Polvani 2011 ). Given this mechanism to generate the jets, we suggest that the higher wind speed for ‘High’ states in our Chemistry simulation fits this complete dynamical picture and the finding of enhanced OzCol in the gyres for ‘High’ states. The simulations show pronounced and vigorous gyres and a strong equatorial jet for ‘High’ states. In contrast, the gyres are less pronounced in the ‘Low’ states, corresponding to less eastward momentum flowing equatorwards, resulting in a substantially weaker jet.

Our results demonstrated the value of compound dynamical systems metrics to elucidate variability in the atmospheres of exoplanets. They can be extended beyond Proxima Centauri b to other Earth-like exoplanets. Our framework also has potential applications with future exoplanet observations, obtained, for example, by the JWST , the Habitable Worlds Observatory, and the Large Interferometer for Exoplanets, since they will contribute to constraining the climate state, dynamics, and potential habitability of Earth-like exoplanets (Hochman et al. 2022 , 2023 ; Quanz et al. 2022 ). Indeed, understanding how ozone impacts climate dynamics and its observations on exoplanets is crucial for grasping the potential habitability of distant worlds. Ozone plays a vital role in shielding an exoplanet from harmful UV radiation. The presence or absence of ozone can provide valuable insights into the composition and stability of exoplanets’ atmospheres. By studying ozone and its interactions within different atmospheric environments, we can interpret atmospheric signatures observed in exoplanet atmospheres, helping us to identify conditions conducive to life as we know it (Cole et al. 2020 ; Ben-Israel et al. 2024 ). Furthermore, understanding ozone dynamics aids in predicting how atmospheric changes, both natural and anthropogenic, may impact habitability on Earth and beyond, guiding our search for potentially habitable exoplanets in the vast Universe. As a caveat, we acknowledge the fact that the actual radius of Proxima Centauri b is unknown because no transit has been detected so far (Kipping et al. 2017 ). Therefore, the planet may not be an Earth-like exoplanet (Brugger et al. 2017 ). We envisage future works on the impact of an entire interactive chemistry module on the climate dynamics of Earth-like exoplanets, with the case study being, for instance, Proxima Centauri b and TRAPPIST-1e. In addition, future work should also include a variety of host stars and FUV/NUV ratios and the effect of varying initial O 2 abundances.

PDL was funded by the European Union's Horizon Europe Research and Innovation Program under Grant Agreement 101059659. MB is part of the CHAMELEON MC ITN EJD, which received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement no. 860470. The Israel Science Foundation (grant #978/23) funds the contribution of AH. We gratefully acknowledge using the MONSooN2 system, a collaborative facility supplied under the Joint Weather and Climate Research Programme, as a strategic partnership between the Met Office and the Natural Environment Research Council. The simulations were performed as part of the project space ‘Using UKCA to investigate atmospheric composition on extra-solar planets (ExoChem)’ with Principal Investigator Paul Palmer.

The authors declare no competing interests.

The time series of the compound dynamical systems’ metrics are available upon reasonable request to the corresponding author.

Anglada-Escudé G. et al.  2016 , Nature , 536 , 437 10.1038/nature19106

Archibald A. T. et al.  2020 , Geosci. Model. Dev. , 13 , 1223 10.5194/gmd-13-1223-2020

Barnes R. 2017 , Celest. Mech. Dyn. Astron. , 129 , 509 10.1007/s10569-017-9783-7

Ben-Israel M. , Holder R. M. , Nelson L. L. , Smith E. F. , Kylander-Clark A. R. C. , Ryb U. 2024 , Nat. Commun. , 15 , 2892 10.1038/s41467-024-46660-7

Bonferroni C. 1936 . Pubblicazioni Del R. Istituto Superiore Di Scienze Economiche e Commerciali Di Firenze , 8 , 3

Boutle I. A. et al.  2017 , A&A , 601 , A120

Braam M. , Palmer P. I. , Decin L. , Cohen M. , Mayne N. J. 2023 , MNRAS , 526 , 263 10.1093/mnras/stad2704

Braam M. et al.  2022 , MNRAS , 517 , 2383 10.1093/mnras/stac2722

Brown A. R. , Beare R. J. , Edwards J. M. , Lock A. P. , Keogh S. J. , Milton S. F. , Walters D. N. 2008 , Boundary Layer Meteorol. , 128 , 117 10.1007/s10546-008-9275-0

Brugger B. , Mousis O. , Deleuil M. , Deschamps F. 2017 , ApJ , 850 , 93 10.3847/1538-4357/aa965a

Chapman A. 1930 . London Edinburgh Dublin Phil. Magaz. J. Sci. , 10 , 369

Chen H. , Wolf E. T. , Kopparapu R. , Domagal-Goldman S. , Horton D. E 2018 , ApJ , 868 , L6 10.3847/2041-8213/aaedb2

Chen H. , Zhan Z. , Youngblood A. , Wolf E. T. , Feinstein A. D. , Horton D. E. 2021 , Nat. Astron. , 5 , 298 10.1038/s41550-020-01264-1

Cohen M. , Bollasina M. A. , Palmer P. I. , Sergeev D. E. , Boutle I. A. , Mayne N. J. , Manners J. 2022 , ApJ , 930 , 152 10.3847/1538-4357/ac625d

Cohen M. , Bollasina M. A. , Sergeev D. E. , Palmer P. I. , Mayne N. J. 2023 , Planet. Sci. J. , 4 , 68 10.3847/PSJ/acc9c4

Cole D. B. , Mills D. B. , Erwin D. H. , Sperling E. A. , Porter S. M. , Reinhard C. T. , Planavsky N. J. 2020 , Geobiology , 18 , 260 10.1111/gbi.12382

Cooke G. J. , Marsh D. R. , Walsh C. , Black B. , Lamarque J.-F. 2022 , R. Soc. Open Sci. , 9 , 211165

Cooke G. J. , Marsh D. R. , Walsh C. , Rugheimer S. , Villanueva G. L. 2023 , MNRAS , 518 , 206 10.1093/mnras/stac2604

Delrez L. et al.  2022 , A&A , 667 , A59

De Luca P. , Messori G. , Faranda D. , Ward P. J. , Coumou D. 2020a . Earth Syst. Dyn. , 11 , 793 10.5194/esd-11-793-2020

De Luca P. , Messori G. , Pons F. M. E. , Faranda D. 2020b . Q. J. R. Meteorolog. Soc. , 146 , 1636

Des Marais D. J. et al.  2002 , Astrobiology , 2 , 153 10.1089/15311070260192246

Domagal-Goldman S. D. , Segura A. , Claire M. W. , Robinson T. D. , Meadows V. S. 2014 , ApJ , 792 , 90 10.1088/0004-637X/792/2/90

Dopplick T. G. 1972 , J. Atmos. Sci. , 29 , 1278 10.1175/1520-0469(1972)029<1278:RHOTGA>2.0.CO;2

Edwards J. M. , Slingo A. 1996 , Q. J. R. Meteorolog. Soc. , 122 , 689 10.1002/qj.49712253107

Faranda D. , Messori G. , Yiou P. 2017 , Sci. Rep. , 7 , 41278

Faranda D. , Messori G. , Yiou P. 2020 , Clim. Dyn. , 54 , 2187 10.1007/s00382-019-05106-3

Faria J. P. et al.  2022 , A&A , 658 , A115

Fishman J. , Ramanathan V. , Crutzen P. J. , Liu S. C. 1979 , Nature , 282 , 818 10.1038/282818a0

France K. et al.  2016 , ApJ , 820 , 89 10.3847/0004-637X/820/2/89

Freitas A. C. M. , Freitas J. M. , Todd M. 2010 , Probab. Theory Relat. Fields , 147 , 675 10.1007/s00440-009-0221-y

Gillon M. et al.  2017 , Nature , 542 , 456 10.1038/nature21360

Godolt M. et al.  2015 , Planet. Space Sci. , 111 , 62 10.1016/j.pss.2015.03.010

Gregory D. , Rowntree P. R. 1990 , Mon. Weather Rev. , 118 , 1483 10.1175/1520-0493(1990)118<1483:AMFCSW>2.0.CO;2

Hammond M. , Lewis N. T. 2021 , Proc. Natl. Acad. Sci. , 118 , e2022705118 10.1073/pnas.2022705118

Hochman A. , Alpert P. , Harpaz T. , Saaroni H. , Messori G. 2019 . Sci. Adv. , 5 , eaau0936 10.1126/sciadv.aau0936

Hochman A. , Alpert P. , Kunin P. , Rostkier-Edelstein D. , Harpaz T. , Saaroni H. , Messori G. 2020 , Clim. Dyn. , 54 , 561 10.1007/s00382-019-05017-3

Hochman A. , De Luca P. , Komacek T. D. 2022 , ApJ , 938 , 114 10.3847/1538-4357/ac866f

Hochman A. , Komacek T. D. , De Luca P. 2023 , Sci. Rep. , 13 , 11123 10.1038/s41598-023-38026-8

Isaksen I. S. A. et al.  2009 , Atmos. Environ. , 43 , 5138 10.1016/j.atmosenv.2009.08.003

Kipping D. M. et al.  2017 , AJ , 153 , 93 10.3847/1538-3881/153/3/93

Komacek T. D. , Abbot D. S. 2019 , ApJ , 871 , 245 10.3847/1538-4357/aafb33

Kossakowski D. et al.  2023 , A&A , 670 , A84

Kozakis T. , Mendonça J. M. , Buchhave L. A. 2022 , A&A , 665 , A156

Lock A. P. , Brown A. R. , Bush M. R. , Martin G. M. , Smith R. N. B. 2000 , Mon. Weather Rev. , 128 , 3187 10.1175/1520-0493(2000)128<3187:ANBLMS>2.0.CO;2

Loyd P. et al.  2016 , ApJ , 824 , 102 10.3847/0004-637X/824/2/102

Lucarini V. , Faranda D. , Wouters J. 2012 , J. Stat. Phys. , 147 , 63 10.1007/s10955-012-0468-z

Mann H. B. , Whitney D. R. 1947 , Ann. Math. Stat. , 18 , 50 10.1214/aoms/1177730491

Masson-Delmotte V. et al.  2021 , IPCC, 2021: Summary for Policymakers: Climate Change 2021–The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change . Cambridge University Press , Cambridge, United Kingdom and New York, NY, USA

Google Scholar

Google Preview

Mayne N. J. et al.  2014 , A&A , 561 , A1

Mayne N. J. et al.  2014 , Geosci. Model. Dev. , 7 , 3059 10.5194/gmd-7-3059-2014

McCulloch D. et al.  2023 , Geosci. Model. Dev. , 16 , 621 10.5194/gmd-16-621-2023

Morgenstern O. , Braesicke P. , O'Connor F. M. , Bushell A. C. , Johnson C. E. , Osprey S. M. , Pyle J. A. 2009 , Geosci. Model. Dev. , 2 , 43 10.5194/gmd-2-43-2009

O'Connor F. M. et al.  2014 , Geosci. Model. Dev. , 7 , 41 10.5194/gmd-7-41-2014

Park J. H. , London J. 1974 , J. Atmos. Sci. , 31 , 1898 10.1175/1520-0469(1974)031<1898:OPARHO>2.0.CO;2

Pierrehumbert R. T. , Hammond M. 2019 , Annu. Rev. Fluid Mech. , 51 , 275 10.1146/annurev-fluid-010518-040516

Proedrou E. , Hocke K. 2016 , Earth Planets Space , 68 , 96 10.1186/s40623-016-0461-x

Quanz S. P. et al.  2022 , A&A , 664 , A21

Ramanathan V. et al.  1987 , Rev. Geophys. , 25 , 1441 10.1029/RG025i007p01441

Ridgway R. J. et al.  2023 , MNRAS , 518 , 2472 10.1093/mnras/stac3105

Rodriguez J. E. et al.  2020 , AJ , 160 , 117 10.3847/1538-3881/aba4b3

Schwieterman E. W. et al.  2018 , Astrobiology , 18 , 663 10.1089/ast.2017.1729

Segura A. et al.  2005 , Astrobiology , 5 , 706 10.1089/ast.2005.5.706

Segura A. et al.  2003 , Astrobiology , 3 , 689 10.1089/153110703322736024

Selsis F. , Despois D. , Parisot J.-P. 2002 , A&A , 388 , 985

Sergeev D. E. , Lambert F. H. , Mayne N. J. , Boutle I. A. , Manners J. , Kohary K. 2020 , ApJ , 894 , 84 10.3847/1538-4357/ab8882

Showman   A. P. , Polvani L. M. , 2011 , Astrophys. J. , 738 , 71

Showman A. P. , Wordsworth R. D. , Merlis T. M. , Kaspi Y. , Dotson R. 2013 , in Mackwell S. J. , Simon-Miller A. A. , Harder J. W. , Bullock M. A. , eds, Comparative Climatology of Terrestrial Planets . University of Arizona Press , Tucson , p. 277 . Retrieved from http://www.jstor.org/stable/j.ctt183gz90.17

Smith A. K. , Marsh D. R. , 2005 , J. Geophys. Res.: Atmos. , 110 , D23305 10.1029/2005JD006298

Snedecor G. W. , Cochran W. G. 1989 , Statistical Methods (8th ed.). Iowa State University Press , Ames, IA

Suissa G. , Mandell A. M. , Wolf E. T. , Villanueva G. L. , Fauchez T. , Kopparapu R. k. 2020 , ApJ , 891 , 58 10.3847/1538-4357/ab72f9

Turbet M. et al.  2016 , A&A , 596 . A112

Vakrat E. , Hochman A. 2023 , Q. J. R. Meteorolog. Soc. , 149 , 3593 10.1002/qj.4575

Wedler M. , Pinto J. G. , Hochman A. 2023 , Sci. Total Environ. , 870 , 161883 10.1016/j.scitotenv.2023.161883

Wilson D. R. , Bushell A. C. , Kerr-Munslow A. M. , Price J. D. , Morcrette C. J. 2008 , Q. J. R. Meteorolog. Soc. , 134 , 2093 10.1002/qj.333

Wood N. et al.  2014 , Q. J. R. Meteorolog. Soc. , 140 , 1505 10.1002/qj.2235

Yang J. , Cowan N. B. , Abbot D. S. 2013 , ApJ , 771 , L45 10.1088/2041-8205/771/2/L45

Yates J. S. , Palmer P. I. , Manners J. , Boutle I. , Kohary K. , Mayne N. , Abraham L. 2020 , MNRAS , 492 , 1691 10.1093/mnras/stz3520

Youngblood A. et al.  2016 , ApJ , 824 , 101 10.3847/0004-637X/824/2/101

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