To quantify the effects of different fertilization rates and basal-to-topdressing ratios on nitrogen uptake and aboveground biomass accumulation of foxtail millet under film-mulched micro-drip irrigation within the “four-in-one” system in northern Shaanxi; to establish critical nitrogen dilution curves under different basal-to-topdressing ratios; to evaluate the applicability of a Bayesian hierarchical model for parameter estimation of the curves; and to determine the optimal fertilization rate and basal-to-topdressing ratio based on the nitrogen nutrition index and yield response, thereby providing a theoretical basis for precise nitrogen management under integrated water-fertilizer conditions in dryland regions of northern Shaanxi.

A two-year field experiment (2023-2024) was conducted in Yulin, Shaanxi Province, using drip irrigation and fertigation treatments. Three basal-to-topdressing fertilizer ratios were set: B82 (8:2), B64 (6:4), and B46 (4:6), along with four fertilizer application levels of N-P₂O₅-K₂O (0-0-0, 90-45-45, 120-60-60, and 150-75-75 kg·hm^-2). The effects of NPK rates and basal-to-topdressing ratios on the aboveground dry matter and nitrogen concentration of millet under supplemental irrigation were investigated. Classical statistical analysis and Bayesian hierarchical modeling were employed to establish critical nitrogen dilution curves and to determine optimal fertilization strategies.

The B64 treatment effectively promoted nitrogen uptake and aboveground biomass accumulation, with overall trends of B64>B82>B46 treatment for both dry matter and nitrogen concentration. Although the basal-to-topdressing ratio had no statistically significant effect on the parameters of the critical nitrogen dilution curve, years with lower precipitation resulted in higher dilution coefficient (A₂) values and increased parameter uncertainty in the B46 treatment. On this basis, the critical nitrogen dilution curves under different basis tracking treatments in 2023, 2024 were proposed: B82: Nc=3.58W^-0.48, Nc=3.14W^-0.36; B64: Nc=3.51W^-0.40, Nc=3.65W^-0.37; and B46: Nc=3.79W^-0.62, Nc=2.71W^-0.36 under different basis tracking treatments. The nitrogen nutrition index (NNI) calculated from these curves increased with fertilization rate, approaching 1.0 at 120-60-60 kg·hm^-2, where relative yield (RY) also reached its maximum. Considering both biomass and yield performance, the optimal fertilizer application rate for millet under these conditions was 120-60-60 kg·hm^-2, with the best basal-to-topdressing ratio of 6:4.

Critical nitrogen dilution curves for foxtail millet under different basal-to-topdressing ratios in northern Shaanxi were developed using both Bayesian and classical statistical methods. The Bayesian approach yielded lower uncertainty and higher precision. By integrating multiple indicators, the optimal basal-to-topdressing ratio was determined to be 6:4, with an N-P₂O₅-K₂O rate of 120-60-60 kg·hm^-2 recommended as the suitable fertilization regime for local foxtail millet production.