You don't need to flood rice fields. You can flood rice fields, which makes it convenient to grow rice in wet places where you can't grow other crops (and which also helps keep away pests and weeds - plus, your paddies can double as fish farms!) - but rice can grow just fine on dry land.

You also don't need to grow potatoes under soil. Potatoes will grow very happily in a basket with a little bit of soil, and then you can keep dumping straw or leaves or compost or whatever over the lowermost leaves whenever they pop up.