Simulation and spatio-temporal dynamics of winter oilseed rape development in China based on nonlinear temperature response

International crop models have been developed using European and American spring oilseed rape varieties. However, the adaptability of these models is limited when applied to winter oilseed rape in China, due to the nonlinear temperature responses associated with vernalization requirements. In this study, a nonlinear temperature-driven development model was proposed to improve the simulation accuracy at the developmental stages using the Temperature-Accumulated day (TAd) algorithm of the Chinese AgroMeteorological Model (CAMM). An exponential temperature efficiency coefficient $k_T\text{=exp(-}k\times T_A)$ was introduced to quantify the nonlinear temperature response. The improved model was calibrated and termed eTAd (exponential TAd). Phenological and meteorological data were captured from 85 agro-meteorological stations over 12 winter oilseed rape-producing provinces during 2000–2024. A grid search method was employed to optimize the temperature efficiency parameter k for different developmental stages. The optimal k values were determined as 0.06 for the emergence-to-anthesis stage, 0 for the anthesis-to-maturity stage, and 0.04 for the sowing-to-emergence stage (where k=0 reduced the eTAd model to the original TAd). Regional simulations were conducted using the China Meteorological Administration Land Data Assimilation System (CLDAS). Meteorological data were gridded at 5 km resolution in the period of 2009–2024. Parameter regionalization was implemented using an improved spatial interpolation, LABdIDW, with the latitude, altitude, and base distance as weighting factors. Mean absolute error was reduced by 5.0% for the thermal threshold parameter at the emergence-to-anthesis stage interpolation, compared with the conventional inverse distance weighting (IDW). The performance of the eTAd model was evaluated using both back-substitution and independent-sample validation. The values were closely comparable at all growth stages; Specifically, the RMSE values were 8.89 and 9.10 d, and the coefficients of determination (R²) were 0.64 and 0.60, respectively, at the emergence-to-anthesis stage, indicating better extrapolation without significant overfitting. Compared with the original TAd model (k=0), the eTAd model reduced the RMSE from 10.00 to 8.89 d at the emergence-to-anthesis stage, with an 11.1% reduction. The best performance was obtained in the high-temperature zone, with an RMSE reduction of 16.77% (from 11.81 to 9.83 d), followed by the moderate-temperature zone (10.46%), while the low-temperature zone exhibited only a minor change (0.89%). The deviation of the original model was correlated with high-temperature zones. The thermal threshold parameter exhibited a “high in the south, low in the north” latitudinal pattern at the emergence-to-anthesis stage, indicating the physiological mechanism that warmer southern regions required greater heat accumulation for anthesis due to incomplete vernalization. The high values were found in the thermal threshold parameter for the anthesis-to-maturity stage in the Yunnan Plateau, the Sichuan Basin, and the middle and lower reaches of the Yangtze River, indicating the heat stress effects on grain filling. The anthesis date advanced significantly at a rate of 0.97 d/a (P<0.01) during 2009–2024, equivalent to an accumulated advancement of 14 days over the 17-year period. The maturity date exhibited significant advancement at a rate of 0.77 d/a (P<0.05) during 2015–2024, while the emergence date showed no significant trend. The regional disparities of anthesis were observed in Sichuan, Yunnan, and Henan provinces, while Jiangsu and Anhui showed no significant trends. The maturity date shared a north-south divergence, where Jiangsu exhibited a significant delay, whereas Hubei and Sichuan shared significant advancements. The emergence-to-maturity duration also shortened significantly at a rate of 0.30 d/a (P=0.016). These phenological variations led to a restructured growth period, where the vegetative phase shortened markedly. The eTAd model can provide a reliable tool to simulate winter oilseed rape developmental stages. The phenological patterns can offer valuable insights into variety zoning, sowing date adjustment, and flowering-period tourism services under climate change.