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Yessica Asmin (22) was swept away on Monday while crossing the swollen Pompolona Creek, which feeds the Clinton River.
Her body was found by searchers on Wednesday afternoon.
In a statement issued through police yesterday, her family said they were devastated by the loss of their daughter.''
Yessica had come to New Zealand for a trip and was only starting her young life, expecting to graduate with her masters degree in marketing from the University of New South Wales in June.''
The family hoped she was the ''last victim in that area of Fiordland''.''
They also hope that those who look after the Milford Track take every step possible so this kind of tragedy does not happen again.''
The Indonesian family passed on their sincere thanks to all who had supported them, including Fiordland SAR, LandSAR, Te Anau police, Southern Lakes Helicopters, Indonesian and New Zealand Embassies, mortuary and funeral services staff.
They also thanked her tramping companions, who had tried to save her.
Ms Asmin was walking with her boyfriend, Sean McNabb, and another tramperat the time.
Sean's mother, Anita McNabb, who frequently visits New Zealand with her husband, said she wanted to stress that isolated parts of the country must be treated with respect and consideration for the weather and terrain.
She said her son was a very experienced tramper and it took only a moment for things to become dangerous. This week's tragedy highlighted the need for caution at rivers, the Mountain Safety Council (MSC) says.
A German tourist with Miss Asmin and Mr McNabb (26) told the Sydney Morning Herald Mr McNabb was overpowered by the water.
Heavy rain in the area caused the Clinton River to peak at 2.2m on Tuesday night; the normal operational safe level was 0.25m.
MSC Outdoor Land Safety programme manager Nathan Watson said any period of heavy rain could result in waterways rising rapidly, meaning even the smallest side stream could present ''considerable challenges''.''
We want more people to go into the outdoors ... However, these experiences need to be safe and in order to do that they require careful planning and smart decision making.''
Friends and family expressed their shock through condolences messages posted on Mr McNabb's Facebook page yesterday.
Anita Howie said she was ''broken''.''
I can feel her spirit ... My adopted daughter ... rest in peace my angel.''
The New Zealand Outdoor Safety Code:
Plan your trip: Seek local knowledge, plan the route you will take, as well as the time you can reasonably expect it to take.
Tell someone your plans and complete an Outdoors Intentions form before leaving. They are available online through www.adventuresmart.org.nz. At the very least tell a friend or family member your plans and a set them a time to raise the alarm if you have not returned by then.
Be aware of the weather: New Zealand's weather can be highly unpredictable. Check forecasts but also expect changes. Check hut and track conditions and be careful of crossing rivers - if in doubt, stay out. Don't be swept away.
Know your limits: Challenge yourself within physical limits and experience.
Take sufficient supplies: Make sure you have enough food, clothing, equipment and emergency rations for a worst-case scenario. Take and know how to use either a mountain radio or a personal locator beacon (PLB).