Leaders of Commonwealth nations are meeting in London this week instead of the South Pacific nation of Vanuatu because things did not go according to plan. In 2015, cyclone Pam roared across Vanuatu, knocking out power, crippling water systems and levelling homes, schools and churches.

In only 24 hours, the storm dashed the island nation’s hopes of hosting the Commonwealth summit. Three years later, many communities have yet to fully recover, in a place where the impact of a changing climate is on full display.

Vanuatu is one of New Zealand’s Pacific neighbours and friends – and its experience is an increasingly common one. In February, Tonga was hit by its worst cyclone in decades, cyclone Gita. When I visited the country in March, I spent time with schoolchildren who were learning in tents – the roof of their school had been blown off and the classroom walls destroyed by the storm.

Cyclone Gita: Tonga devastated by worst storm in 60 years Read more

Such extreme weather events are tragedies. They are also provocations. They tell us that climate change is not a theory, or a projection, but something that is already happening. They tell us we must be more ambitious when it comes to tackling this urgent global challenge.

The Commonwealth heads of government meeting is a good place to start. Twenty-eight years ago, the same meeting produced the Langkawi declaration on the environment, among the first collective statements to cite greenhouse gas emissions as one of the chief problems facing the world. I am confident that this year’s gathering can be just as decisive by fostering bold commitments to step up climate action.

And while the task ahead is immense, New Zealanders know it can be achieved because we have a proud history of leadership on challenges than can seem too hard to contemplate.

We were the first country in which women won the right to vote, we were at the forefront of the anti-nuclear movement, and we were at the table when the United Nations was born. And we are ready to lead on climate change, the defining challenge of our generation.

That is why my government has committed to setting an ambitious new target of achieving carbon neutrality by 2050. In June, we are starting a consultation process on how to enshrine this commitment in law.

Our plan includes an expert Independent Climate Commission which will develop carbon budgets through to 2050 – setting a path to carbon neutrality that maintains enough energy to run our economy and country. Along the way, we are committed to helping regions and industries directly affected by the transition move away from fossil fuels, with billions of dollars of investment in local infrastructure and clean energy projects on the horizon.

New Zealand plans to achieve 100% renewable electricity generation by 2035

We are also active in building international cooperation on climate action.

Nearly half of New Zealand’s emissions come from our world-renowned farming sector. This is why we lead the 49-nation Global Research Alliance that is developing techniques to reduce agricultural emissions without compromising food security. And that is why we are committed to helping other countries achieve more climate-friendly agricultural production, in ways that will increase farmers’ yields and build resilience while reducing emissions.

Alongside the UK, we belong to coalitions of forward-thinking countries and cities pressing to phase out coal generation, eliminate harmful subsidies that encourage wasteful fossil fuel use, and help our economies transition to carbon neutrality.

The international consensus on climate change in Paris in 2015 was a historic achievement. Now we all need to do our part by delivering on what we signed up to.

This means setting ambitious and concrete goals, like New Zealand’s plan to achieve 100% renewable electricity generation by 2035. And it means agreeing on the finer details around holding countries accountable for reaching their Paris targets.

Leadership on climate change cannot be left to the big economies. It demands broad and deep action. New Zealand contributes less than 1% of global emissions. Yet together the world’s small emitters account for about a quarter of global emissions. History calls on us to play our part.

At this week’s Commonwealth meeting, I’ll be thinking about Vanuatu’s experience – and the summit that couldn’t happen. I’ll also be guided by a Māori saying from my country – Mō tātou, ā, mō kā uri, ā muri ake nei – for us and for our children after us.

That is what’s at stake when we talk about climate change – the world we’ll leave for the generations that follow us. They are why we need to act now, with purpose and courage.

• Jacinda Ardern is the prime minister of New Zealand