New Zealand were forced to make one change from the side that won the first test by an innings and 49 runs in Auckland with Ish Sodhi replacing fellow leg-spinner Todd Astle, who suffered a side strain.
"It looks like a good surface but with an early morning start and a little bit of moisture around (it might help the bowlers)," Williamson said.
"It does tend to brown off and become a good surface so that's the logic behind that."
The match has been overshadowed by the ball-tampering furore in South Africa, but New Zealand's first test victory, just their 10th overall against England, has put them in a position to beat England in a series for the first time since 1999.
England had already dropped off-spinning all-rounder Moeen Ali and bowler Chris Woakes also paid the price for a lack of penetration in Auckland despite showing his batting ability with a second-innings half century.
Batsman James Vince was restored to the side, fast bowler Mark Wood replaced Woakes and left-arm spinner Jack Leach will make his test debut.
"We've just changed things around to try and give ourselves the best combination to take 20 wickets and with the bat make sure we get 400 plus," England captain Joe Root said.
"We just have to make sure that we look to go on and make a big first-innings score ... so its important we play the first two hours very well."
Root will return to number four in the batting order and it is still uncertain whether all-rounder Ben Stokes will be able bowl.
Stokes injured his back during the one-day series and did not bowl in Auckland.
"It's a day by day (case)," Root added of Stokes's injury.
"Hopefully we will see some progression but it's something we have to manage."
New Zealand - Kane Williamson (captain), Jeet Raval, Tom Latham, Ross Taylor, Henry Nicholls, BJ Watling, Colin de Grandhomme, Tim Southee, Ish Sodhi, Neil Wagner, Trent Boult.
England - Joe Root (captain) Alastair Cook, Mark Stoneman, James Vince, Dawid Malan, Ben Stokes, Jonny Bairstow, Stuart Broad, Mark Wood, Jack Leach, James Anderson
(Reporting by Greg Stutchbury in Wellington; Editing by Ed Osmond)
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