Auckland-based lawyer Tama Hovell, acting for the two hapu, outlined the grounds for the appeal in his Notice of Appeal lodged with the High Court on January 30.
He said the Environment Court in its interim decision last year had erred in law by finding that it had no jurisdiction to require removal of the wreck.
The court was ruling on the appeal to the Bay of Plenty Regional Council's original decision to leave the remains of the Rena on the reef.
The grounds for the High Court appeal included the section of the Environment Court's interim decision which said the court had no power ''to require the removal of the wreck from the reef''.
It was an interim decision because Judge Jeff Smith left it up to all the parties involved in the Environment Court hearing to consult on the conditions of consent. The parameters of the conditions were set out in the judge's decision.
Hovell said that in the context of an application to abandon the wreck, there was no jurisdictional bar on the Environment Court requiring the removal of the wreck as conditions of the consent.
His Notice of Appeal said there had been procedural errors, including that the site visit out to the reef by the members of the court had been ''used for a purpose which was not conveyed to the parties''.
''The observation relied on from the site visit conflicted with the expert evidence given in the hearing. The observation was not put to the relevant expert witness,'' Hovell said.
He quoted the interim decision where it stated: ''We noted that, on the day of our site visit to the reef, schools of fish were present, as were many seabirds and a pod of dolphins.''
Judge Smith said it led to the court's expert in tikanga Maori, Commissioner Prime, to say that the mana had been returned to Tangaroa - the Maori deity of the sea.
''Given the evidence we have heard and what we saw ourselves, we are persuaded that the reef is recovering its mauri,'' the decision said.
Hovell responded in the Notice of Appeal that the reliance by the court or Commissioner Prime on the site visit was an improper use of the site visit.
He said it was not a matter put to the parties during the hearing or the relevant expert witnesses. The use of the site visit for this purpose conflicted with the two hapu's expert witness on tikanga Maori.
The Notice of Appeal also stated that the Environment Court had erred in law by ''dismissing past effects associated with the original wreck and its aftermath''.
It said the court did not apply the proper legal test and erred by dismissing effects on people and communities based on the cultural conditions that affected them.
Key dates in Rena disaster
October 5, 2011: Ship hits Astrolabe Reef 2.20am.
October 10, 2011: Oil starts washing ashore on Tauranga beaches.
January 2012: Rena breaks in half.