Functional Data Analysis of Sentinel-2 Derived Vegetative Phenology for Potato Yield Estimation Under Normal and Cyclone Conditions

Sentinel-2 derived vegetative phenology indicators, such as the Normalized Difference Vegetation Index (NDVI), have been effective at predicting potato yields, but earlier approaches relied on a single approach, ignoring the whole seasonal pattern. In this study, we used functional data analysis (FDA) on NDVI time series from 47 smallholder fields across two seasons: one affected by a cyclone in 2021–22 and the other a normal season in 2022–23. Cyclone Jawad brought 137 mm of rain in early December 2021, more than twice the usual rainfall, causing delays in sowing. The NDVI data were collected across both seasons and then smoothed separately using penalized cubic B-splines. A permutation-based functional t-test showed that NDVI patterns differed significantly between the two seasons, especially early in the season, suggesting that crop establishment was delayed in 2021–22. The scalar-on-function regression (SoFR) models for each season, using a functional generalized additive model (FGAM), were applied to assess whether the two patterns had significant effects on yield. Adjusted R²=0.238 with p=0.016 for the 2021–22 season and adjusted R²=0.283 with p=0.013 for the 2022-23 season revealed that the full NDVI pattern was a significant predictor of yield. In 2021–22, yield increased steadily with NDVI, whereas in 2022–23, yield peaked during mid-season canopy closure. A bootstrap test confirmed that these differences in the relationship between NDVI and yield were significant, suggesting that models trained in normal years may not work well in years with extreme weather. The FDA provides a way to detect and measure these changes, which can help improve remote-sensing yield forecasts in regions affected by climate change.