One way to deal with water that drains from roof is to build a seasonal creek using gravel and rock. It is important that the level of the seasonal creek is below the foundation of the house, see drawing. Allow the water to exit the downspout into a drain in the usual way. Dig out the location of the seasonal creek , which can meander around until it reaches the street, or preferably stop in a low point in the garden. The banks of the streambed should be stabilized by rock or broken concrete. Line the bottom with four inches of coarse gravel or pebbles so that the water can flow cleanly. Planting the edge of the streambed with grasses and other plants will enhance the natural appearance. In summertime or when the streambed is dry the it should be cleaned of leaves and debris to maintain an attractive appearance year-round.
If the stream ends at a low spot in the garden, the end point might be widened to emulate a small pond and a large boulder or two can be embedded in the gravel bottom.