Improving SOC estimation in low-relief farmlands using time-series crop spectral variables and harmonic component variables based on minimum sample size

Efficiently monitoring Soil Organic Carbon (SOC) in farmlands is crucial for environmental and agricultural sustainability. Currently, crop spectral variables are primarily employed to estimate SOC in low-relief farmlands. To enhance SOC estimation, further crop information needs to be excavated. Additionally, few studies have considered the sample size in modeling SOC estimation, which may lead to precision loss and cost waste. Therefore, this study proposed a novel method to improve SOC estimation in low-relief farmlands. This method considers more information on crop growth and minimum sample size. The results showed that: (1) time-series NDVI was established as the characteristic crop spectral variables, based on crop spectral variables extracted from eight-day time-series reflectance products. (2) Seventeen harmonic component variables were derived from time-series NDVI via Fourier transformation. (3) Six crop spectral variables and seven harmonic component variables were determined as the optimal SOC estimators. (4) The convolutional neural network model provided higher SOC estimation accuracy (R² = 0.81, NRMSE = 7.09%) than the random forest model and the back propagation neural network model. And the minimum sample size based on the optimal model was determined to be 250. (5) The proposed method improved SOC estimation at the regional scale, achieving a 2.54% reduction in NRMSE compared to the NDVI-based model. These findings suggest that the proposed method holds the potential for efficient SOC estimation in low-relief farmlands.