The floods on Friday also destroyed about 2,000 houses, and damaged thousands more homes and businesses
"We've got a long way to go to get a good total," Hashim Amla said after his 50 and an unbeaten 33 from Faf du Plessis helped the Proteas recover from a disastrous start on a rain-disrupted day in which only 41 overs were possible.
From being five for two in the fourth over, South Africa were 123 for four at stumps while New Zealand had blown their review opportunities.
"There is so much time left," Amla said with South Africa maintaining a win was still possible despite rain forecast for the remaining four days. "We want to bat as long as we can in the first innings to get a really big score on the board to set the game up."
They have the advantage of knowing New Zealand have no reviews left before the 80th over which has already cost them the chance to remove du Plessis.
Just 13 balls after using up their second review they were powerless to react when the umpires missed a faint edge which should have seen du Plessis caught behind for 16.
New Zealand quick Matt Henry described the weather and faulty reviewing as "frustrating" but said the hosts were still satisfied with their day's work.
"We did well to get them four down. We didn't get (the reviews) right. It can be frustrating but we get another chance later on," he said. South Africa, starting the Test with an unbeatable 1-0 series lead, were two down in the fourth over after winning the toss and electing to bat.
It would have been three for 28 if not for the first New Zealand judgement error of the day.
They decided not to review a rejected Neil Wagner lbw appeal against JP Duminy on seven when the ball tracker technology signalled a direct hit.
Duminy went on to make 20 in a 59-run stand for the third wicket with Amla before being removed just before lunch.
Amla went soon after the break for 50, his 32nd half-century and was left 67 runs short of becoming the fourth South African to total 8,000 career runs.
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