Optimum water and nitrogen supply regulates root distribution and produces high grain yields in spring wheat (Triticum aestivum L.) under permanent raised bed tillage in arid northwest China

•Root growth and distribution responses to N fertilizer depended on the quantity of irrigation.•2400 m3 ha−1 of irrigation and 180 kg N ha−1 N resulted in deep root system.•Less or more irrigation and N fertilizer reduced the yield, water and N use efficiencies and root length density of spring wheat.•2400 m ha−1 of irrigation and 180 kg N ha−1 produced highest grain yield and water and N use efficiencies under permanent raised tillage in arid northwest China.