Modelling of heat stress in a robotic dairy farm. Part 4: Time constant and cumulative effects of heat stress

Heat stress is usually assessed using thermal comfort indices (TCIs) that calculate integrated values of temperature, humidity, wind speed and solar radiation. However, the negative effect of heat stress is related not only to the intensity but also the duration of heat stress endured, as well as the accumulated influence from previous time periods. This study was conducted to develop adjusted TCIs which could simultaneously quantify the intensity and duration of heat stress. The data for this study came from production and climate data collected on a robotically milked dairy-farm. Thresholds of heat stress under diurnal pattern (0–24 h) and lag pattern (−90 to 0 d) for different TCIs were identified to be related to a significant decrease of daily milk yields (DMY). An intensity duration index (IDI) was proposed to evaluate daily short-term heat stress (HIDI) and heat stress relief (RIDI), by multiplying the percentage difference between TCIs and their threshold values (i.e. intensity) by the duration. Thresholds of HIDI and RIDI, as well as their sum i.e. IDItotal were identified to describe multiple levels of heat stress with different significant decrease rate of DMY from −0.01 to −0.05 kg∙cow−1∙d−1[DMY]∙(%∙h)−1[IDI]. To evaluate the long-term lag and cumulative effects of heat stress, TCIs with weighted cumulative adjustment (TCIWCE) and heat stress adjustment (TCIHS) were defined by assigning a different level of importance to daily TCIs of the previous period and calculating the average of these weighted TCIs. Multiple linear regressions between DMY and adjusted TCIs (i.e. TCIWCE and TCIHS) were performed considering age, body mass (BM) and days in milk (DIM) as basic independent variables. The adjusted R squared (R2) and residual root mean square (RMS) values of these regressions were used for comparison. Using adjustment TCIWCE or TCIHS was found to increase the adjusted R2 and decrease RSS, indicating an improved explanation of variance in heat stress impact