The NZ Climate Science Coalition is made up of people who are sceptical about global warming and share concerns about "misleading information" on climate change, according to the website.
The dispute relates to readings from the "Seven-station Series" (7SS) - stations in Auckland, Masterton, Wellington, Nelson, Hokitika, Lincoln and Dunedin - used by Niwa for national temperature records.
The trust says unscientific methods were used to reach the results, creating an unrealistic indication of climate warming.
"We're not saying climate change doesn't exist. We're saying let's at least make sure that evidence of this for New Zealanders is accurate," trust lawyer Terry Sissons told the court today.
He challenged the way Niwa had adjusted temperatures recorded at stations, which he said were moved half a degree downwards on average in early readings.
The results had significantly affected the overall upwards rise in temperature, said Mr Sissons.
"Is that valid that you can expose a trend, simply by pushing down the readings in the early part to make them colder? Then when you compare them to the modern ones you get a steep increase."
Instead of using the accepted international method to estimate how site changes had affected temperature and rainfall, Niwa instead used the untested techniques of former employee James Salinger, said Mr Sissons..
Niwa had said it had used the accepted scientific method for later data but evidence "strongly supports they didn't", Mr Sissons said.
In Auckland, measurements from Albert Park in the CBD and Mangere make up some of the data used in the seven-station temperature series.
Spikes in temperature at those and other sites could be attributed to factors such as changes to shelter and urbanisation, rather than climate change, Mr Sissons said.
At Albert Park for example, tree growth would have altered shelter at the station over time, he said.
The disputed climate data had been used for a number of projects, had a "profound effect" on policy making, and was also used to predict future trends, he said.
The trust is asking the court to invalidate the temperature record, to stop Niwa from using the the record to advise the Government and the public and for Niwa to provide "full and accurate" temperature record.
In a statement posted on the trust's website prior to today's hearing, spokesman Brian Leyland said he believed it was the first time official temperature records had been challenged in court.
"Many scientists believe that, although the earth has been in a natural warming phase for the past 150 years, it has not heated as much as Government archives claim. The precise trend figure is extremely important, as it forms the sole basis of the claim that human activities are the dominant cause of the warming."
The hearing, being heard by Justice Geoffrey Venning, has been set down for a week.
