I am not talking about sophisticated stuff such as central pivot, sprinkler, drip, qanat, aquifer based, etc, but more about just surface level irrigation with small channels and such. How widely spaced do the channels need to be? How would they be arranged? Would they directly come out of rivers and streams? Where would the water go in the end? Would the river itself irrigate any land just through water infiltrating through the soil?
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On the island of Madeira many levadas have been built along the contours of the mountains. These collect rain on the wetter windward side of the island and channel it around to the leeward side where there is much less rain. The people pay to have wooden slats removed from the side of the levada for a certain amount of time each day/week to allow water to run out of the levada and down onto their farmland below. As you can probably guess there’s a lot of variety in how irrigation works.