Optimizing Biochar Rate and Particle Size for Enhanced Wheat Yield and Water Productivity Using Response Surface Methodology

• Biochar is a promising tool for sustainable management of organic residues. • Simultaneous optimization of wheat yield and irrigation water loss. • Wheat straw biochar effects strongly depend on application rate. • Response surface method accurately predicted optimal conditions. • Highest yield and minimal water loss at 2.5% biochar and 0.63 mm particle size. Biochar is a promising amendment for improving soil quality and water use efficiency, but its performance depends heavily on application rate and particle size. This study aimed to optimize the combined effects of wheat straw biochar rate and particle size on wheat yield (WY) and irrigation water loss (WL). Experiments were conducted using a central composite design and response surface methodology (RSM). WY and WL were evaluated under biochar levels of 0.5–2.5% by weight and particle sizes of 0.25–1.25 mm. Results revealed that the interactive effects of biochar rate and particle size on both responses were significant and nonlinear. The highest WY and the lowest WL were obtained at a 2.5% application rate with medium-sized particles (model-predicted optimum of approximately 0.63 mm). Under these conditions, WY was markedly increased to 5184.86 kg ha -1 , and WL was minimized to 0.60 m 3 kg -1 . Conversely lower application rates or very fine and coarse particles showed limited effects due to reduced effective surface contact and physical constraints. Validation of the RSM model, demonstrated by a high coefficient of determination (R² = 0.988), confirmed the accuracy and reliability of this approach for predicting and designing optimal biochar application. These findings highlight the importance of simultaneously determining biochar rate and particle size to enhance crop performance and to support sustainable soil and water resource management. This provides a practical framework for improving productivity and advancing sustainable agriculture.