The assistant secretary of the agriculture department, Narelle Clegg, must have approved the export of 58,000 sheep from Western Australia based on “irrational, illogical or unreasonable” information, the federal court has heard.

Animals Australia has taken the federal government to court to argue the export permit granted by Clegg to Emanuel Exports for the voyage was unlawful. The ship is bound for the Middle East and began its voyage on 6 June.

Representing Animals Australia, Dan Star QC, told Justice Debbie Mortimer at hearing in Melbourne that Clegg had been presented with scientific and expert evidence that showed the ship did not meet mandatory requirements for an export permit to be approved.

This included a report from a vet and a meteorologist showing a 50% probability that ambient wet-bulb temperatures during the Indian Ocean part of the journey could reach temperatures of 28C or more for more than one day in a row. This probability rose to 70% for the Persian Gulf part of the journey, Star said.

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These conditions could lead to severe heat stress and death to the animals, he said. But permit requirements mean the secretary needs to be satisfied that the health and welfare of animals will be maintained throughout the course of an export journey.

“It is impossible to be satisfied of these conditions and mandatory requirements,” Star said. “The secretary must have misunderstood the scope of her power ... there is nothing to justify her being satisfied of these requirements ... [her decision] must have involved irrational, illogical, or unreasonable findings.”

Emanuel Exports came under scrutiny in April after footage was aired on 60 Minutes from one of its export ships, the Awassi Express, which showed sheep dying from severe heat stress. The footage, filmed in August 2017, triggered an inquiry into conditions on board export ships during the Middle Eastern summer. Livestock vet Dr Michael McCarthy led the review and made a number of recommendations. In its submission to the review, the Australian Veterinary Association called for a ban on live sheep exports to the Middle East between May and October. The government rejected this recommendation.

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“It gets worse for sheep in July and August,” Star said. “We say that it is urgent for there to be a trial because there is a heat-stress season that runs from May to October.”

Star requested that Clegg provide the court with documents detailing the decision-making process behind granting the permit to Emanuel Exports by 19 June. He said he wanted to see the risk assessment model for heat stress used by the department in making its decision to grant the export permit.

“It should be publicly available or at least provided to us,” he said.

Mortimer responded: “We’re not here on some jurisdictional fact inquiry about the validity of the model.”

A lawyer representing the government told Mortimer “the model contains a software program”. Data was entered into the program, such as the number of livestock and the species. “It produces outcomes which assists in some evaluation of likely occurrence of heat-stress events and mortalities,” he said. “I don’t think the department itself possesses the software program.”

The regulatory regime for exporting livestock was likely to change as early as next week as a result of findings from the McCarthy review, he said, but he did not elaborate on that those changes would be.

The hearing continues.