"With further warming, there's a stronger density step and less nutrient supply for the surface waters so phytoplankton doesn't grow so well and productivity drops down."
This has already happened in the water off Tasmania and the southeast corner of Australia, which is warming rapidly as the East Australian current pushes warmer water further south, causing huge changes to the ecosystem.
Coastal ecosystems were changing and subtropical species increasing, which can affect the economy, Law said.
"We are predicted to get an equivalent amount of warming by the end of the century, so what's happening to the ecosystem off Tasmania might be a good proxy for what we're going to see in New Zealand waters."
The paper reports that one of the most affected areas for nutrient decline will be the Chatham Rise east of New Zealand, which provides about 60 per cent of the country's commercial fish catch.
Another vulnerable area was the subantarctic waters south of New Zealand, which are also home to commercial fisheries.
"All regions will see a reduction in food supply, because of a decrease in particulate material sinking from the surface — and that is what links climate change to our fisheries."
The fishing industry may need to think about being more agile in terms of the species it catches and where it catches them, Law said.
"For example, if fish go deeper to maintain their temperature, they will have to adjust their practices to account for that."
Acidity in the ocean will increase by 130 per cent by the end of the century, which will cause changes to shellfish.
"For example, we can speculate that shells of paua and mussels may be affected — it doesn't mean we lose them from our ecosystems, just that they might become smaller in response to their diversion of energy to maintain their shells."
Changes in species in New Zealand waters could include more invasive species and possibly new diseases that could affect local ecosystems.
However, there may also be an upside.
Tuna could be more plentiful in our waters because they prefer warmer waters and other fisheries may also benefit.
"In New Zealand we're on the border between the warmer water, where things are moving from, and the cooler water, where things are moving to.
"Therefore, we won't be as hard hit as some of the islands in tropical regions where continual warming will reduce numbers of fish and plankton."
He also said the Earth systems models used by the scientists provided the best data "for now" but their global scale meant they provided information at low resolution.
"This paper is a first look at what these models suggest future conditions might be around New Zealand.
"But if we want more information we need to develop our own models that can give us more precision and greater resolution on a spatial scale."
Law said the aim of the paper was to inform the public and policy makers that conditions are going to change.
"People tend to think of climate change from a terrestrial angle but obviously, as the ocean is a big part of the globe, there will be significant changes.
"As it's also a significant part of New Zealand's Exclusive Economic Zone we need to start planning for this now."