Strict Recursive Closed-Loop Evaluation of Greenhouse Air Temperature Forecasting with Generated Exogenous Variables and Exogenous-Error Propagation Analysis.

Accurate multi-horizon forecasting of greenhouse air temperature is essential for sensor-based environmental monitoring and control-oriented decision support. However, conventional evaluation methods often rely on open-loop or semi-closed-loop settings, where future observations may be unavailable during practical deployment. This study established a strict recursive closed-loop forecasting protocol and an exogenous-error propagation analysis framework using multi-source environmental sensing data. A Liquid Neural Network (LNN) was developed as a continuous-time forecasting model and compared with long short-term memory (LSTM), gated recurrent unit (GRU), and extreme gradient boosting (XGBoost) under consistent data conditions. During inference, future greenhouse air temperature and exogenous variables were not observed but recursively generated through predicted-temperature feedback and exogenous-variable forecasting. Across 10 repeated runs, the LNN achieved the lowest one-step prediction error, with a mean absolute error of 0.4771 °C and root mean square error of 0.5996 °C. However, under strict recursive closed-loop forecasting, LSTM showed the lowest errors at 6 h, 24 h, and 48 h horizons, indicating stronger long-horizon stability. Ablation experiments demonstrated that using observed future exogenous variables underestimated forecasting errors, while exogenous-error analysis identified outdoor temperature and solar radiation as the dominant sources of propagated uncertainty. These results highlight the importance of evaluating greenhouse air temperature forecasting under realistic recursive conditions by considering both model stability and future input uncertainty.