Wavelet-based hyperspectral Random Forest modeling of a frost damage severity index (FDSI) in winter wheat

Frost injury at the jointing stage of wheat is among the most destructive abiotic stresses worldwide. It can markedly limit yield formation by reducing the number of productive tillers and suppressing the differentiation of young spikes and florets. However, timely and accurate quantification of frost damage after an event remains difficult because integrated physiological evaluation indices and efficient prediction models are still lacking. To address this issue, we selected four winter wheat cultivars: two frost-sensitive and two frost-tolerant. These plants were subjected to a series of low-temperature treatments at the jointing stage. On the day after frost exposure, we measured 19 physiological and biochemical traits and collected canopy hyperspectral reflectance data. A Frost Damage Severity Index (FDSI) was developed using principal component analysis (PCA) combined with membership function analysis, which enabled the treatments to be classified into five frost-damage levels. To achieve non-destructive assessment of damage severity, we proposed a hyperspectral evaluation framework that integrates original reflectance (OR) with continuous wavelet transform features (WF). Through a Pearson–CARS–VIF hybrid feature-selection strategy, we identified two sensitive spectral bands and four wavelet-sensitive features from the OR and WF datasets. These features were then used to build and compare four machine-learning models, including support vector regression (SVR) and random forest regression (RFR). Among single data types, the WF-RFR model performed best, improving the coefficient of determination ( R ²) by 7% and reducing the root mean square error (RMSE) by 15.99% relative to OR-RFR. After fusing OR and WF, the OR+WF-RFR model further enhanced prediction performance. Compared with WF-RFR, it increased R² by 9.54%, decreased RMSE by 20.14%, reduced mean absolute error (MAE) by 10.07%, and increased the residual predictive deviation (RPD) by 30.49%. SHapley Additive exPlanations (SHAP) analysis indicated that the high-scale wavelet feature WF 829,8 was the primary predictor, capturing early frost-induced changes in micro-scale cellular structure, while R 745 provided critical complementary information. In summary, the proposed FDSI and the OR+WF-RFR model constitute a technical framework for early quantitative assessment of frost damage in winter wheat, with practical value for dynamic field monitoring, screening frost-tolerant cultivars, and supporting precision cultivation management.