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Fiordland residents, in particular, won't welcome the news as they continue to clean up after rain and flooding struck the area last week.
And little of the system's moisture is expected to go where it is needed most – in drought-stricken Auckland and Northland.
A severe weather outlook issued this afternoon covered the bottom of the South Island and parts of the West Coast.
The MetService said there was a moderate chance it would bring severe gales and heavy rain to the areas covered by the outlook.
"There is still some uncertainty regarding the track and intensity of this low, but heavy rain and severe gales are likely to result.
"Significant impacts are possible, and this system will be closely monitored the coming days, and people are urged to stay up to date with the latest forecasts and warnings."
Although Uesi's low centre might not make landfall, rain bands associated with the storm should sweep over the South Island from later on Sunday, possibly bringing heavy falls and severe gales for Fiordland and parts of Westland.
"Even though the storm will no longer be characterised as a Tropical Cyclone by then, the severity of the weather associated with it will still be significant for parts of the country still recovering from recent storms."
Kerr said severe weather warnings were required, these would begin appearing on MetService's website from Friday.
He added that, as the forecast track of this system had changed significantly from yesterday, there was still a level of uncertainty associated with the exact impacts.
But at this stage there was nothing to suggest that the upper North Island would receive any of the rain.
"As the cyclone comes down to the west of the country, that ridge that is over the North Island at the moment is going to move away, and we'll start feeling a little more of an easterly flow."
That could bring warmer, moister conditions – and potentially some showers – but nothing significant enough to break a drought, he said.
WeatherWatch was advising trampers planning to walk in Fiordland and surrounding National Parks to pay close attention to the forecast from Sunday to next Wednesday - and alter plans if necessary.
While it was too early to lock in rainfall totals, preliminary estimates showed between 100mm to 150mm falling for the lower western side of the South Island – and that could potentially double, the website predicted.
It also pointed to the possibility of remnants of the system lingering and reaching the North Island at the end of next week.
"It may only be in the form of showers but Uesi will churn up currents in the atmosphere dragging down more moisture into the Tasman Sea region," WeatherWatch reported.
"There is some modelling showing showers are more likely in the end of February for the North Island."