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.

中文翻译：

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机器人奶牛场热应激建模。第 4 部分：热应激的时间常数和累积效应

热应激通常使用热舒适指数 (TCIs) 进行评估，该指数计算温度、湿度、风速和太阳辐射的综合值。然而，热应激的负面影响不仅与热应激的强度有关，还与热应激的持续时间有关，也与先前时期的累积影响有关。本研究旨在开发可同时量化热应激强度和持续时间的调整后的 TCI。这项研究的数据来自在机器人挤奶的奶牛场收集的生产和气候数据。不同TCI的昼夜模式（0-24小时）和滞后模式（-90至0天）下的热应激阈值被确定与每日产奶量（DMY）的显着降低有关。提出了强度持续时间指数 (IDI) 来评估每日短期热应激 (HIDI) 和热应激缓解 (RIDI)，方法是将 TCI 与其阈值（即强度）之间的百分比差异乘以持续时间。确定了 HIDI 和 RIDI 的阈值以及它们的总和，即 IDItotal 来描述多个水平的热应激，其中 DMY 的显着降低率从 -0.01 到 -0.05 kg∙cow−1∙d−1[DMY]∙(% ∙h)−1[IDI]。为了评估热应激的长期滞后和累积效应，加权累积调整 (TCIWCE) 和热应激调整 (TCIHS) 通过为前一时期的每日 TCI 分配不同的重要性水平并计算平均值来定义 TCI这些加权的 TCI。DMY 和调整后的 TCI 之间的多元线性回归（即 TCIWCE 和 TCIHS) 将年龄、体重 (BM) 和牛奶中的天数 (DIM) 作为基本自变量进行。这些回归的调整后的 R 平方 (R2) 和残余均方根 (RMS) 值用于比较。发现使用调整 TCIWCE 或 TCIHS 会增加调整后的 R2 并降低 RSS，表明对热应力影响差异的改进解释。