An improved maize normalized root length density model based on water consumption and nitrogen application

Understanding maize root distribution is critical for determining the root water uptake zone and improving water and nitrogen (W–N) management. However, direct measurement of root length density (RLD) is labor-intensive and time-consuming, and most existing normalized RLD (NRLD) models lack physical constraints on root distribution. A two-year field experiment (four irrigation × five nitrogen levels) was conducted to quantify the effects of W–N management on spring maize RLD. Results revealed that maize roots exhibited a shallow enrichment and gradual decline with soil depth, with the maximum RLD in the 0–20 cm soil layer. Appropriate W–N management practices promoted deeper root proliferation, enhancing drought resilience. The proposed NRLD model is expressed as a cubic polynomial function that satisfies NRLD = 0 at the maximum rooting depth, integrating maize water consumption and nitrogen application as key predictors of root distribution, ensuring physical significance. It enables estimation of NRLD values at different soil layers can be estimated directly from W–N data and rooting depth without destructive sampling. Model validation using 2024 measured values and published datasets demonstrated good accuracy and applicability across various soil types and growth stages in semi-arid regions (R² ≥ 0.63, RMSE ≤ 0.61, NRMSE ≤ 18.06 %, MAE ≤ 0.46). Additionally, the NRLD model effectively estimated the RLD distribution and vertical root length density allocation under various W–N managements. This study offers a rapid and practical approach for estimating root distribution and promotes sustainable intensification in semi-arid maize production systems.