Is the full tithe, or half of it, due on agricultural land irrigated by well water?

The amount of zakat due on crops and fruits varies depending on the irrigation method: If irrigated by rainwater, springs, or if it is ba'liya (irrigated naturally by its roots without human effort), then one-tenth (10%) is due. The evidence for this is the saying of the Prophet, peace be upon him: "In what is irrigated by the sky and springs, or what is 'athari (naturally irrigated), one-tenth is due." If irrigated with effort and expense (by a machine to lift water), then half of one-tenth (5%) is due. The evidence for this is the saying of the Prophet, peace be upon him: "And in what is irrigated by nadh (manual effort to draw water), half of one-tenth is due."

Based on this: If a farmer digs a well and needs tools to transport water to irrigate the crops, then half of one-tenth is due, because the irrigation was done with effort/expense. However, if the water flows out of the well visibly and reaches the agricultural land without effort, then one-tenth is due, because the cost of digging the well is not considered an expense that affects the amount of zakat, as it is akin to tilling the land and does not recur annually.