Innovative functional modelling framework reveals black globe temperature as the most robust predictor of circadian heat related behavior in grazing dairy cows

Capturing 24‑h behavioral responses to heat stress remains analytically challenging due to strong non‑linearities, individual variability, and the temporal structure of grazing systems. Traditional analyses typically ignore circadian dynamics or assume linear thermal responses, limiting their capacity to detect biologically relevant shifts. We aimed to develop an advanced modelling framework capable of (i) identifying which climatic index best predicts circadian behavioral rhythms under pasture conditions, and (ii) quantifying how rhythms re‑time under hot vs. cool days. We hypothesized that black globe temperature (TBG), integrating radiation and air temperature, would outperform other indices. We analyzed 2.46 million accelerometer‑based behavioral records collected at 5‑min intervals from 86 grazing Holstein cows over two summers. Eight climatic indices were derived from hourly meteorological data. Circadian dynamics of twelve behavioral traits were modelled using big additive models (BAM) with cyclic cubic splines, allowing smooth 24‑h periodicity and scalable computation on large datasets. Each climatic index was tested via a dedicated spline term, and performance was compared using AIC. Days were classified into cool (≤23.6 °C TBG) and hot (≥29.4 °C) based on empirical quantiles, and BAMs were refitted for each class to quantify functional differences in rhythm amplitude, phase, and shape. Confidence bands were used for inference on whole‑curve differences rather than pointwise values, enabling functional comparison of circadian patterns. TBG provided the lowest AIC in 10/12 behaviors, clearly outperforming THI, CCI, HLI, WBGT and other indices. Functional predictions revealed significant, systematic re‑timing of behaviors between hot and cool conditions, as evidenced by non‑overlapping 95% simultaneous confidence intervals across extended time windows. Under heat, cows shifted rumination and resting towards the night–early morning, increased standing in early morning and late afternoon, and reduced midday activity—patterns consistent with circadian thermoregulatory adjustments. These results demonstrate that the BAM‑based functional approach uncovers subtle rhythmic reorganizations that would remain undetected with classical linear or mean‑based analyses. This study introduces a novel, scalable functional modelling pipeline combining BAM, cyclic splines and quantile‑based thermal classification to dissect circadian behavioral responses at high temporal resolution. Black globe temperature emerged as the most reliable environmental driver of circadian dynamics in grazing cows, highlighting the central role of solar radiation in shaping heat‑related behavior. This framework offers a methodological advance for heat‑stress research and provides a transferable tool for evaluating thermal stress in precision livestock systems, especially where large behavioral time‑series and complex non‑linear rhythms must be analyzed.