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The calls came as councillors at yesterday's annual plan deliberations voted to add more than $1 million to the budget, spread over two years, the improve the organisation's ability to plan for climate change.
Several councillors who voted in favour of the spending cited rising community demands for action, as people took to the streets and urged the council to declare a climate emergency.
Cr Aaron Hawkins said young people, in particular, were "fed up'' with the "inadequate'' actions of those in power, including Dunedin city councillors.
Climate change was the "single biggest issue we face'', impacting people, communities, infrastructure and the economy, and decisions over the next few years would be "crucial'', he said.
"Doing nothing at the moment is sending a fairly significant invoice to the people who come after us,'' he said.
Earlier, council corporate policy manager Maria Ioannou explained the funding would enable work to consider whether the council's "business as usual'' approach was preparing the city for climate change, or exposing it to greater risk.
The potential risks varied, from considering whether investment in new pipes or other infrastructure renewals were adequate for climate change scenarios, to identifying other unknown risks that could emerge.
Dunedin Mayor Dave Cull said one example had been highlighted on the Kapiti Coast, where the council had been taken to court by wealthy coastal property owners after adding a warning about sea level rise to LIMs.
The council had been forced to remove it, but now faced the risk of litigation and legal costs from future owners upset the council knew about the risk but did not warn them, Mr Cull said.
Ms Ioannou said the council sometimes seemed to be operating in a "twin universe'' of work on climate change and business as usual, when the two spheres needed to become one.
However, the temperature began to rise as Cr Lee Vandervis questioned the value of the work.
He described it as a "$1million word-fest'' that should be tackled by central government, but was being driven by Labour and Green Party policies and "virtue signalling'' around the council table.
That prompted a point of order from Cr Hawkins and a caution for denigrating staff from Mr Cull, who forced Cr Vandervis to withdraw the comment.
But, when Cr Vandervis tried to persist, Mr Cull had clearly had enough.
"Just be quiet. As I said the other day, you have got two ears and one mouth. That's the proportion in which you should use them.''
Other councillors piled in to support the funding, including Cr Kate Wilson, who said the council would find more areas in need of work, to prepare for climate change, the more it scratched the surface.
Cr Christine Garey said the council needed to shift ``from talk to action'', and a co-ordinated approach was needed.
Cr Jim O'Malley also backed the need for speedy action.
"We are destroying our world quickly and so we do have to act quickly.''
However, Cr Mike Lord also raised eyebrows when he declared he was "not convinced'' human activity was influencing climate change to the extent others thought.
But when he referred to an earlier submission by a "lunatic'' professor who predicted 5m of sea level rise by 2090, he drew a protest from Cr Hawkins and a caution from Mr Cull.
Councillors voted 11-2 to approve the funding, Crs Vandervis and Lord opposed.