Identifying the critical potassium inputs for optimum yield, potassium use efficiency and soil fertility through potassium balance in a winter wheat-summer maize rotation system in North China

Potassium (K) is a primary limiting macronutrient for plant growth. Inappropriate K application decisions can lead to reduced yield and potassium use efficiency (KUE). Given the scarcity and non-renewable nature of K resources, developing an indicator for critical K input is essential. The apparent K balance is a simplified method calculated from fertilizer inputs and crop K uptake, enabling straightforward agronomic evaluation. Here, we hypothesize that the apparent K balance serves as a valuable indicator for determining critical K input. A twelve-year field trial with six K treatments (0, 30, 60, 90, 120, and 150 kg K ha^–1 per year) was conducted to assess grain yield response to apparent K balance, establish a K input-output framework, and determine critical K input in a winter wheat-summer maize rotation system in North China. The crop yield, K uptake, and K fertilizer recovery efficiency initially increased but then declined with increasing K fertilizer rates, likely due to excessive K-induced nutrient imbalance and salt stress. The K balance threshold can be determined based on the target yield to be pursued. A K balance of 0 –9.77 kg K ha^–1 per year achieved optimal yield and maintained soil fertility. The K input-output framework provided a clear visualization of the K balance and KUE relationships. The critical K input range of 56.6 –62.5 kg K ha^–1 achieved high yields with KUE improving to 85 –100 %, while sustaining high levels of soil available K and organic matter. Overall, optimizing K input within appropriate K balance thresholds enhances crop yield, KUE and soil quality simultaneously. This study provides new insights for determining critical K balance and K input, offering guidance for field-scale K management.