Well a climate similar to japan you will need to:
1) in summer: provide a good natural ventilation. Once you empty the tub, wipe it with a dry cloth and leave the windows open.
A wet climate may cause mold stains. On the other hand, this problem is minimized because we use a water repellent. See the documentation on our HP:
http://www.bartokdesign.com/japan/downloads/kihadaichiban-description.pdf

2) in winter: avoid using heating equipment in the bathroom when the tub is empty. Use the tub often (at least 2 times a week) and if you leave for an extended period, leave a bucket of water inside the tub and cover it to increase the air relative humidity. Keep an hygrometer near the tub and assure that humidity does not drop below 50%.
If the climate is too dry, there is the risk of the wood drying and eventually cracking.