Identifying Environmental Response Windows in Cabbage Growth Using Smart-Farm Data

This study identifies environmental response windows in cabbage growth using daily smart-farm data from April to July 2025. Crop growth responses to environmental conditions may occur immediately, with delay, or through cumulative interactions over time, making a single fixed lag structure potentially restrictive. To address this issue, the study compares fixed-lag Granger causality, variable lag Granger causality with Dynamic Time Warping (DTW), and sparse lag selection models. The analysis focuses on two cabbage growth outcomes, weight growth and leaf growth, and five environmental variables: temperature range, humidity, rainfall, insolation, and average wind speed. The results show that fixedlag Granger causality provides useful benchmark evidence but is sensitive to the imposed lag order. DTW based variable lag diagnostics indicate flexible temporal alignment, particularly for leaf growth, but delay direction diagnostics suggest that many alignments are difficult to interpret as causal timing evidence. Sparse lag-selection provides clearer evidence of specific environmental response windows. In the basic sparse model, humidity at lag 13 is negatively selected for both weight growth and leaf growth, while temperature range at lag 9 is positively selected for both outcomes. In the growth stage controlled model for weight growth, temperature range is positively selected at lags 3, 9, 11, and 12; rainfall is negatively selected at lags 3 and 4; humidity shows mixed lagged associations; and average wind speed is selected at lag 6. These findings suggest that sparse lag selection can complement DTW based variable lag analysis by identifying specific lag positions relevant to smart farm crop growth monitoring and decision support.