MS-HyTimeXer: a stem sap flow prediction model integrating multi-scale temporal features

Objective Stem sap flow is a key indicator for quantifying plant transpiration and evaluating ecosystem water use efficiency. Its dynamics are jointly influenced by environmental factors, physiological regulation, and time-lag effects, making it difficult for conventional prediction methods to effectively characterize complex nonlinear relationships and medium- to long-term variations. To address the limitations of existing time series forecasting models in multi-scale feature extraction and modeling the lagged response of plant water transport, this paper proposes MS-HyTimeXer, a medium- to long-term stem sap flow prediction model based on a multi-scale hybrid Transformer.

Method Based on stem sap flow observations of Pinus strobus in eastern Canada from the SAPFLUXNET database, continuous 30 min interval data from January 1, 2010 to December 31, 2011 were selected, yielding a total of 35 040 samples for the experiments. Built upon the TimeXer model, three key modules were introduced: multi-scale patch embedding, LSTM temporal calibration, and multi-scale convolution. Multi-scale patch embedding enhances the representation of features across different temporal scales; LSTM temporal calibration captures the time-lag relationship between environmental changes and sap flow response; and multi-scale convolution extracts local abrupt changes and short-term dynamic features. Five models, including DLinear, Informer, PatchTST, iTransformer and TimeXer, were chosen as baseline methods to evaluate the prediction performance of different models.

Result Experimental results demonstrated that MS-HyTimeXer effectively integrated multi-scale temporal features and environmental factor information, achieving optimal performance in medium- to long-term stem sap flow prediction. Compared with the baseline TimeXer model, the mean squared error (MSE) of MS-HyTimeXer decreased from 0.765 cm³/(cm²·h) to 0.312 cm³/(cm²·h), a reduction of 59.74%; the coefficient of determination (R²) increased from 0.869 to 0.918; and the mean absolute percentage error (MAPE) dropped to 7.652%. Among the six deep learning models, MS-HyTimeXer attained the lowest MSE, MAE, and MAPE, exhibiting superior prediction accuracy and stability. Further analysis revealed that the model still maintains competitive performance in medium- to long-term prediction tasks when the prediction window length reached 512.

Conclusion By integrating multi-scale temporal representation, long-term dependency modeling, and local dynamic feature extraction mechanisms, MS-HyTimeXer effectively improves stem sap flow prediction capability under complex eco-environmental conditions, offering a new technical approach for plant transpiration estimation, forest water resource management, and intelligent ecosystem monitoring.