Optimal use of water and fertilizers can enhance winter wheat yield and increase the efficiencies of water and fertilizer usage in dryland agricultural systems.In order to optimize water and nitrogen(N)management for winter wheat,we conducted field experiments from 2006 to 2008 at the Changwu Agro-ecological Experimental Station of the Chinese Academy of Sciences on the Loess Plateau,China.Regression models of wheat yield and evapotranspiration(ET)were established in this study to evaluate the water and fertilizer coupling effects and to determine the optimal coupling domain.The results showed that there was a positive effect of water and N fertilizer on crop yield,and optimal irrigation and N inputs can significantly increase the yield of winter wheat.In the drought year(2006–2007),the maximum yield(Ymax)of winter wheat was 9.211 t/hm2for the treatment with 324 mm irrigation and 310 kg/hm2N input,and the highest water use efficiency(WUE)of 16.335 kg/(hm2 mm)was achieved with198 mm irrigation and 274 kg/hm2N input.While in the normal year(2007–2008),the maximum winter wheat yield of 10.715 t/hm2was achieved by applying 318 mm irrigation and 291 kg/hm2N,and the highest WUE was 18.69kg/(hm2 mm)with 107 mm irrigation and 256 kg/hm2N input.Crop yield and ET response to irrigation and N inputs followed a quadratic and a line function,respectively.The optimal coupling domain was determined using the elasticity index(EI)and its expression in the water-N dimensions,and was represented by an ellipse,such that the global maximum WUE(WUEmax)and Ymax values corresponded to the left and right end points of the long axis,respectively.Considering the aim to get the greatest profit in practice,the optimal coupling domain was represented by the lower half of the ellipse,with the Ymax and WUEmax on the two end points of the long axis.Overall,we found that the total amount of irrigation for winter wheat should not exceed 324 mm.In addition,our optimal coupling domain visually reflects the optimal range of water and N inputs for the maximum winter wheat yield on the Loess Plateau,and it may also provide a useful reference for identifying appropriate water and N inputs in agricultural applications. Optimal use of water and fertilizers can enhance winter wheat yield and increase the efficiencies of water and fertilizer usage in dryland agricultural systems. In order to optimize water and nitrogen (N) management for winter wheat, we conducted field experiments from 2006 to 2008 at the Changwu Agro-ecological Experimental Station of the Chinese Academy of Sciences on the Loess Plateau, China. Regression models of wheat yield and evapotranspiration (ET) were established in this study to evaluate the water and fertilizer coupling effects and determine the optimal coupling domain. The results showed that there was a positive effect of water and N fertilizer on crop yield, and optimal irrigation and N inputs can significantly increase the yield of winter wheat. The drought year (2006-2007), the maximum yield (Ymax) of winter wheat was 9.211 t / hm2 for the treatment with 324 mm irrigation and 310 kg / hm2N input, and the highest water use efficiency (WUE) of 16.335 kg / (hm2 mm) was achieved with198 mm i rrigation and 274 kg / hm2N input. Temperature in the normal year (2007-2008), the maximum winter wheat yield of 10.715 t / hm2was achieved by applying 318 mm irrigation and 291 kg / hm2N, and the highest WUE was 18.69 kg / ( hm2 mm) with 107 mm irrigation and 256 kg / hm2N input. Crop yield and ET response to irrigation and N inputs followed by a quadratic and a line function, respectively. The optimal coupling domain was determined using the elasticity index (EI) and its expression in the water-N dimensions, and was represented by an ellipse, such that the global maximum WUE (WUEmax) and Ymax values ​​are corresponded to the left and right end points of the long axis, respectively.Considering the aim to get the greatest profit in practice, the optimal coupling domain was represented by the lower half of the ellipse, with the Ymax and WUEmax on the two end points of the long axis. Overall, we found that the total amount of irrigation for winter wheat should not exceed 324 mm. In addition, our optimal coupling domain visually refl ectsthe optimal range of water and N inputs for the maximum winter wheat yield on the Loess Plateau, and it may also provide a useful reference for identifying appropriate water and N inputs in agricultural applications.