A Queensland university that unlawfully sacked a professor for criticising colleagues for their research on the impact of global warming on the Great Barrier Reef is back in court

James Cook University is appealing the Brisbane Federal Circuit Court's finding that it contravened the Fair Work Act when it dismissed Peter Vincent Ridd in 2018.

Judge Salvatore Vasta made 28 findings in April 2019 against the university, which censured Prof Ridd for remarks against a coral researcher, the Australian Institute of Marine Science and the ARC Centre of Excellence for Coral Reef Studies.

The university was later ordered to pay Prof Ridd more than $1.2m for lost income, lost future income and other costs.

Before sacking the geophysicist, the university alleged Prof Ridd had violated its code of conduct during an August 2017 interview on Sky News when he remarked some of the university's research could "no longer be trusted".

It also alleged Prof Ridd wrote of a researcher in an email to a student: "It is not like he has any clue about the weather. He will give the normal doom science about the (Great Barrier Reef)".

Judge Vasta found the university's actions, including the dismissal, were unlawful.

"Incredibly, the university has not understood the whole concept of intellectual freedom," he wrote in his findings.

"In reality, intellectual freedom is the cornerstone of this core mission of all institutions of higher learning."

Freedom of expression and the interpretation of the university's code of conduct were the focus of the appeal submissions on Tuesday.

The university's lawyer, Bret Walker SC, said the university was responsible for enforcing standards of behaviour to protect intellectual freedom and the code of conduct.

Mr Walker said staff had the right to intellectual freedom and the right to express certain views but not bully, harass or intimidate others.

"Freedom .... is not without limit, restriction or standard," he told the court.

The two-day hearing continues.

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