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Dairy Cow Thermal Balance Model During Heat Stress: Part 2. Model Assessment
Kevin A. Janni1,*, Chad R. Nelson1, Bradley J. Heins2, Kirsten Sharpe2
Published in Journal of the ASABE 66(2): 461-468 (doi: 10.13031/ja.15191). Copyright 2023 American Society of Agricultural and Biological Engineers.
1Bioproducts and Biosystems Engineering, University of Minnesota, St. Paul, Minnesota, USA.
2West Central Research and Outreach Center, University of Minnesota, Morris, Minnesota, USA.
*Correspondence: kjanni@umn.edu
The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Submitted for review on 16 May 2022 as manuscript number PAFS 15191; approved for publication as a Research Article by Associate Editor Dr. Lingjuan Wang-Li and Community Editor Dr. Jun Zhu of the Plant, Animal, & Facility Systems Community of ASABE on 26 January 2023.
Highlights
Abstract. A steady-state process-based lactating cow thermal balance spreadsheet model developed by Nelson and Janni (in press) was compared to mean measured body temperatures, respiration rates, and skin temperatures from two published studies (Gebremedhin et al., 2010; Chen et al., 2015). Model body temperatures were also compared with reticular temperatures from cows standing in unshaded paddocks that were part of a solar shade study (Sharpe et al., 2021). Gebremedhin et al. (2010) reported measured mean rectal temperatures, 39.4 ± 0.5 C and 40.6 ± 0.4 C for hot and dry conditions with and without a solar load; model body temperatures for similar hot and dry conditions were 39.7 C and 40.6 C with and without a solar load, respectively. Model respiration rates were within one standard deviation of measured mean respiration rates (Gebremedhin et al., 2010). The model body temperature for a baseline condition was 39.1°C, which was within 0.1°C of the mean baseline temperature of 39.2 ± 0.6°C (Chen et al., 2015). The model respiration rate was 63 breaths per minute (bpm); much lower than the reported baseline respiration rate of 88 bpm (Chen et al., 2015). Model body temperatures were 0.1°C to 0.7°C lower than the measured mean reticular temperatures of standing cows in non-shaded paddocks with solar loads when ambient temperatures ranged from 24.4°C to 26.5°C. Model results compared well with mean measured parameters from three studies. The model can be used to assess the impact of factors affecting heat exchange (e.g., body mass, milk yield, solar load, air dry-bulb temperature, dew-point temperature, and air velocity) on heat exchange flux, cow respiration rate, and body temperature.
Numerous researchers have developed models and relations to describe how lactating cows balance metabolic heat production and heat exchange via shortwave radiation, respiration, convection, longwave radiation, and evaporation to maintain body temperatures in acceptable ranges during heat stress (McGovern and Bruce, 2000; Berman, 2005; McArthur, 1987; Turnpenny et al., 2000a, b; Thompson et al., 2014). Nelson and Janni (in press) used these studies, a ground temperature relation from Gwadera et al. (2017), new empirical relations for tissue insulation and sweat rate, and a new solution method to develop a process-based thermal balance model for lactating cows solved using a spreadsheet. The model can be used to assess factors that impact heat stress in lactating cows and practices to mitigate heat stress.
Model validation against measured data is an important step to building confidence in model results. McGovern and Bruce (2000) reported that they did not find data to validate their model. Berman (2005) modified the McGovern and Bruce (2000) model to incorporate information for Holstein cows and reported that respiratory frequencies were highly correlated with equations derived by Stevens (1981). Berman (2005) also reported that his modified model had changes in rectal temperature that were closely related to those of shaded Holstein cows from several studies (Berman, 1968; Berman and Morag, 1971; Berman et al., 1985; Igono et al., 1987; and Her et al., 1988). Berman (2005) also reported that respiratory frequency and rectal temperatures corresponded well to data from Roman-Ponce et al. (1977). McArthur (1987) compared model body temperature and respiration rate results with data from Jersey cows (Worstell and Brody, 1953) and noted that the model predicted realistic responses to changing air temperatures. Turnpenny et al. (2000b) compared their model results for sensible and latent heat loss with measured values for beef steers from Blaxter and Wainman (1964) and other animal species (e.g., sheep, swine, and chickens). Thompson et al. (2014b) evaluated their model (Thompson et al., 2014a) against data for Bos indicus and Bos taurus and reported that model skin temperature, body temperature, sweating rate, and respiration rate relations aligned closely with published data (Allen, 1962; Brown-Brandl et al., 2003; 2005; Finch, 1985).
Thermal balance models for lactating cows that effectively describe thermal processes and relations between inputs and outputs can be used to identify critical factors that impact how well cows are able to manage their body temperatures during heat stress (Thompson et al., 2014b). Thompson et al. (2014b) also noted a need for more complete data including skin and body temperatures, sweating and respiration rates, respiratory evaporation losses, and radiation fluxes. A complete dataset was not found in the literature, but recent work has published physiological data from a controlled indoor chamber study (Gebremedhin et al., 2010), an outdoor study of cows cooled with sprinklers (Chen et al., 2015) and cows on pasture in the sun (Sharpe et al., 2021).
The overall goal of this project was to develop a model that quantitatively described heat exchange between a lactating Holstein and her surrounding environment during warm and heat stress conditions. The purpose of this article, which is a companion to the model development article by Nelson and Janni (in press), is to compare the model results to recently published measured data for heat stressed, lactating cows from Gebremedhin et al. (2010) and Chen et al. (2015), and reticular temperatures from grazing cows (Sharpe et al., 2021).
Model Assessment Data
The steady-state thermal balance model developed by Nelson and Janni (in press) has over 15 inputs, 18 coefficients, and over 85 calculated intermediate values and results. There are no known studies with all the values needed to validate the model. This article used average data from two published studies (i.e., Gebremedhin et al., 2010, Chen et al., 2015) and unpublished data from a shade study (Sharpe et al., 2021).
Table 1 lists the model input information collected from Gebremedhin et al. (2010) and Chen et al. (2015). In table 1, the spaces marked “NA” indicate unavailable data and where assumed values were needed. Table 2 lists the assumed model constants and coefficients used when measured values were not available or reported as described by Nelson and Janni (in press).
| Table 1. Model information from Gebremedhin et al. (2010) and Chen et al. (2015), used to assess the thermal balance model.[a] | ||
| Model Input | Gebremedhin et al. (2010) | Chen et al. (2015) |
| Cow mass | NA | 643 kg |
| Milk yield | 41.7 kg d-1 | 39 kg d-1 |
| Milk fat | NA | NA |
| Atmospheric pressure | NA | NA |
| Solar radiation | 0 or 550 W m-2 | 0 W m-2 |
| Ambient dry-bulb temperature | 29.1°C or 35.1°C | 31.2°C |
| Ambient air moisture level | 69.2% or 23.1% Relative humidity | 20.4°C Wet-bulb temperature |
| Wind/Air speed | 1 m s-1 | 1.7 m s-1 |
| Mid cow height | NA | NA |
[a] NA = Not available. | ||
| Table 2. Assumed constant model inputs and coefficients used in the model if not reported in the data set. | |
| Variable Description | Value |
| Cow mass | 600 kg |
| Milk fat | 3.5% |
| Mid cow height | 1.0 m |
| Cow surface area exposed | 100% |
| Cow body heat capacity | 3,400 J kg-1 K-1 |
| Coat insulation | 0.3 C m2 d Mcal-1 mm-1 |
| Ground convection coefficient | 33 W m-2 K-1 |
| Ground evaporation flux | 52 W m-2 |
| Ground longwave radiation flux | 63 W m-2 |
| Ground emissivity | 0.9 |
| Albedo | 0.25 |
| Atmospheric pressure | 100,230 Pa |
| Longwave exposure factor | 1 |
| Minimum tissue resistance | 0.016 m2 K W-1 |
| Minimum sweat rate | 14.4 g m-2 h-1 |
| Maximum sweat rate | 660 g m-2 h-1 |
| Coat thickness | 3.0 mm |
| Coat reflectivity | 0.3 |
| Coat emissivity | 0.98 |
| Heat storage time | 3 h |
| Normal cow body temperature | 38.0°C |
| Atmospheric dispersion factor | 0.1 |
A coat reflectivity value of 0.3 was used for all cases involving a solar load (table 2). The value corresponded to a cow that was 50:50 black and white, following the practice used by Turnpenny et al. (2000b). Model results do not distinguish between black and white coat colors.
Gebremedhin et al. (2010)
Gebremedhin et al. (2010) measured sweating rates, respiration rates, skin temperatures, and rectal temperatures of 12 high-producing multiparous Holstein cows held in an environmental chamber. Measurements were collected multiple times during either hot and dry conditions or hot and humid conditions with and without a solar load. Sweating rates and skin temperatures were measured on the dorsal area. For the hot and humid conditions, the average air temperature was 29.1°C and the relative humidity was 69.2%. For the hot and dry conditions, the average air temperature was 35.1°C and the relative humidity was 23.1%. For both conditions, the air velocity in the chamber was 1 m s-1, and the temperature humidity index (THI) was 78. The solar load from solar lamps when present was 550 W m-2.The average reported milk yield was 41.7 ± 2.5 kg d-1. A mean radiant temperature of the surroundings when no solar load was applied was assumed to be 3°C above the dry-bulb temperature.
Chen et al. (2015)
Chen et al. (2015) reported measured baseline intravaginal body temperatures, respiration rates, and skin temperatures of 18 high-producing lactating pregnant Holstein-Friesian cows coming from a home pen with shaded, sand-bedded free stalls with fans. The mean and standard deviation of cow body weights were 643 ± 58 kg, and daily milk yields were 39 ± 4 kg d-1.
Daily weather conditions between 13:00 and 14:00 h as well as 14:45 and 15:45 h on experimental days in June through August 2011 at the University of California-Davis dairy facility were reported by Chen et al. (2015). Air dry-bulb temperature ranged from 20.6°C to 38.9°C with a mean and standard deviation of 31.2 ± 3.8°C. Wet bulb temperatures ranged from 15.6°C to 22.7°C with a mean and standard deviation of 20.4 ± 1.5°C. The wind speed ranged from 0.4 to 4.1 m s-1 with a mean and standard deviation of 1.7 ± 0.8 m s-1, and solar radiation ranged from 338 to 874 W m-2 with a mean and standard deviation of 798 ± 64 W m-2. Mean conditions were used as model inputs. The corresponding mean dew-point temperature used was 12.6°C. Averaged pretreatment data were used in the model.
It was assumed that the cows had 100% shading in the home pen prior to moving to the experimental area. The mean radiant temperature was assumed to be 5°C above ambient dry-bulb temperature to account for the heating of surrounding surfaces by solar insolation.
Morris Data Inputs (Sharpe et al. 2021)
A third data set used in the model had measured reticular temperatures averaged over an hour from 24 individual cows, ambient weather conditions, and solar insolation levels while cows were grazing during sunny periods from a study to assess model results for cows in sunshine (Sharpe et al., 2021). Not all of the data used in the thermal balance model was published by Sharpe et al. (2021).
Sharpe et al. (2021) reported cow characteristics (i.e., milk yield, fat and protein production, and drinking bouts), cleanliness, reticular temperatures, and respiration rates of 24 crossbred cows of a low-input grazing herd in four treatment groups. Two groups had access to pasture paddocks for grazing with shade from photovoltaic solar collectors, while two groups had access to pasture paddocks without shade from solar collectors, trees, or buildings for four periods ranging from 5 to 7 days long in June through September 2019. Weather data (i.e., dry-bulb temperature, percent humidity, and horizontal solar irradiation) was recorded automatically every 15 min with a weather station at the West Central Research and Outreach Center (WCROC, Morris, MN) located at 45°35'44? N and 95° 52'53? W (HOBO RX3000 Data Logger and Weather Station, Onset Computer Corp., Bourne, MA) and downloaded at the end of each study period (Sharpe et al., 2021).
All cows had a CowManager ear tag sensor (CowManager SensOors, Agis, Harmelen, the Netherlands). The ear tag sensor data was used to identify ruminating, eating, not active, active, and highly active behaviors (Pereira et al., 2018). Agis Automatisering BV (Agis, Harmelen, the Netherlands) provided processed hourly data from the CowManager sensor. SmaXtec boluses (smaXtec Classic Bolus, Graz, Austria) were administered orally to each cow 1 week before the first study period (Sharpe et al., 2021). Boluses, which recorded internal body temperature in the reticulum every 10 minutes, were downloaded weekly. Reported bolus temperature accuracy was ± 0.25°C (Ammer et al., 2016). Daily milk production from individual cows was measured with a Boumatic Smart Dairy system (Madison, WI), and fat, protein, and SCC were measured and recorded each month during the study. Milk samples were analyzed by Stearns DHIA Laboratories (Sauk Centre, MN, USA) with a 4000/5000 Combi-Foss Milk Analyzer (Hillerød, Denmark). Cow body weight was recorded at the beginning and end of each study period using a digital scale as cows exited the milking parlor. Mid cow heights were determined using cow mass and ASABE Standard D321.2 Dimensions of Livestock and Poultry (2020). More data collection details are available in Sharpe et al. (2021).
The data for the cows in the two groups with access to the solar panel shade was not able to specify if the cows were in the shade or not; therefore, the data for the shade groups animals were not used. The CowManager data for the cows without shade was screened to find 1-hour periods when the data indicated that a cow was eating, active, or highly active for 57 or more minutes. The hourly weather data were screened to find hours with the warmest weather. Finally, the smaXtec data were screened to confirm that there were no indications of cows drinking three hours prior to the hours with active and eating cows during hot weather. After screening the cow activity, weather, and reticular temperature data, ten cases were identified among the 20 days of data where one or more cows were eating, active, or highly active for more than 57 minutes per hour during warm weather (table 3). The ten cases occurred for five hours during the study period.
Temperatures during the study period produced limited heat stress (Sharpe et al., 2021). Dry-bulb temperatures for the ten cases found for model analysis ranged from 19.6°C to 25.5°C, and dew-point temperatures ranged from 5°C to 21°C.
Wind speed and barometric pressure data were not available from the weather station at the WCROC. Wind speed and barometric data from St. Cloud, MN, approximately 150 km east of the WCROC, were used as inputs in the model.
Results and Discussion
Repeated measurements with normal distributions are commonly reported with means and standard deviations. The three studies used to assess the model reported means and standard deviations. The model was deemed to provide very accurate information when the model results were within one standard deviation of the measured mean.
Gebremedhin et al. (2010) Results
The mean values and standard deviations of the measured sweating rates, respiration rates, rectal temperatures, and skin temperatures reported by Gebremedhin et al. (2010) for both hot and humid conditions and hot and dry conditions are given in table 4. Model results for the corresponding conditions and outputs are also listed in table 4.
Sweating Rates
Gebremedhin reported that mean measured sweating rates for individual cows ranged from 185.0 to 205.7 g m-2 h-1 for the hot and humid treatment and 173.6 to 337.4 g m-2 h-1 for the hot and dry treatment with and without the solar load. The sweating rate standard deviation ranged from ± 90.7 to ± 159 g m-2 h-1 across both the hot and humid conditions and the hot and dry conditions (Gebremedhin et al., 2010). Gebremedhin et al. (2010) also observed that sweating rates were cyclical and seemed to follow skin temperature.
The steady-state model sweating rates were 191 to 240 g m-2 h-1 for the hot and humid treatment and 243 to 295 g m-2 h-1 for the hot and dry treatment with and without the solar load, respectively. All model sweating rates were within one standard deviation of the measured mean for both the hot and humid conditions and the hot and dry conditions (table 4), which indicated the model described sweating accurately. Accurate sweating rates are important in the model because evaporated sweat represented 48% to 71% of the total heat exchange for the four environmental chamber conditions (i.e., hot and humid without solar load, hot and humid with solar load, hot and dry without solar load, and hot and dry with solar load).
Respiration Rates
Gebremedhin et al. (2010) reported mean measured respiration rates for the hot and humid treatment as 71.7 and 114 bpm for the without and with solar load cases, respectively. For the hot and dry treatment, the mean measured respiration rates were 95.8 and 107.3 bpm for the without and with solar load cases, respectively. Respiration rate standard deviations were 14.4 and 12.4 bpm for the hot and humid treatment and 15.0 and 13.0 bpm for the hot and dry treatment for the without and with solar load cases, respectively (Gebremedhin et al., 2010).
| Table 3. Model inputs used from ten hours of Morris data from five cows for the thermal balance model collected as part of a pasture shade study (Sharpe et al., 2021). | ||||||||||||||||||
| Case | Cow ID | Day Hour | Cow Mass (kg) | Milk Yield (kg d-1) | MilkFat (%) | Mid Cow Height (m) | Air Dry-Bulb Temp (°C) | Air Dew-Point Temp (°C) | Air Velocity at Cow Mid Height[a] (m s-1) | Solar Radiation (W m-2) | Atmospheric Pressure[b] (Pa) | |||||||
| 1 | 1762 | 10 Jun 13:00 | 442 | 18.8 | 3.9 | 0.95 | 25.5 | 19.2 | 5.6 | 877 | 98,375 | |||||||
| 2 | 1762 | 10 Jul 13:00 | 440 | 12.2 | 3.9 | 0.95 | 25.0 | 18.2 | 4.5 | 893 | 97,223 | |||||||
| 3 | 1631 | 10 Jul 13:00 | 417 | 14.8 | 5.1 | 0.95 | 25.0 | 18.2 | 4.5 | 893 | 97,223 | |||||||
| 4 | 15103 | 10 Jul 13:00 | 544 | 18.4 | 3.9 | 1.0 | 25.0 | 18.2 | 4.5 | 893 | 97,223 | |||||||
| 5 | 15103 | 12 Aug 13:00 | 579 | 11.3 | 4.7 | 1.0 | 24.4 | 21.0 | 2.9 | 755 | 97,460 | |||||||
| 6 | 1513 | 12 Aug 13:00 | 637 | 16.8 | 3.1 | 1.0 | 24.4 | 21.0 | 2.8 | 755 | 97,460 | |||||||
| 7 | 1715 | 12 Aug 13:00 | 515 | 9.6 | 5.3 | 0.98 | 24.4 | 21.0 | 2.8 | 755 | 97,460 | |||||||
| 8 | 1715 | 13 Aug 14:00 | 515 | 11.7 | 5.3 | 0.98 | 22.8 | 18.6 | 2.8 | 309 | 97,562 | |||||||
| 9 | 15103 | 18 Sep 14:00 | 585 | 13.1 | 4.1 | 1.0 | 19.6 | 5.0 | 7.3 | 740 | 97,291 | |||||||
| 10 | 1631 | 18 Sep 140:0 | 458 | 9.3 | 4.9 | 0.95 | 19.6 | 5.0 | 7.3 | 740 | 97,291 | |||||||
[a] From St. Cloud, MN, and adjusted for mid cow height using Power law, ucow = uw · (hm / 10)p , for wind speed, uw , measured at 10 m height, input mid cow height, hm = 1 m, and exponent, p = 0.1, for stability class C and smooth surface (Cooper and Alley, 2011). [b]From St. Cloud, MN. | ||||||||||||||||||
Table 4. Model results and measured means and standard deviations of four physiological responses of 12 cows with and without solar exposure during either hot and humid conditions or hot and dry conditions (Gebremedhin et al. 2010). | ||||||||||||||||||
| Hot and Humid Conditions | Hot and Dry Conditions | |||||||||||||||||
| Mean ± Standard Deviation | Model Results | Mean ± Standard Deviation | Model Results | |||||||||||||||
| Sweating rate (g m-2 h-1) | No solar load, black hair | 205.7 ± 105.4 | 191 | 173.6 ± 123.2 | 243 | |||||||||||||
| With solar load, black hair | 185.0 ± 131.5 | 240[a] | 291.7 ± 159.0 | 295[a] | ||||||||||||||
| With solar load, white hair | 205.7 ± 90.7 | 337.5 ± 158.6 | ||||||||||||||||
| Respiration rate (Breaths per minute) | No solar load | 71.7 ± 14.3 | 70 | 95.8 ± 15.0 | 84 | |||||||||||||
| With solar load | 114 ± 12.4 | 106 | 107.3 ± 13.0 | 118 | ||||||||||||||
| Body temperature (°C) | No solar load | 38.8 ± 0.3 | 39.3 | 39.4 ± 0.5 | 39.7 | |||||||||||||
| Solar load | 39.6 ± 0.6 | 40.3 | 40.6 ± 0.4 | 40.6 | ||||||||||||||
| Skin temperature (°C) | No solar load, black hair | 33.9 ± 0.8 | 36.4 | 36.5 ± 0.7 | 37.0 | |||||||||||||
| With solar load, black hair | 37.7 ± 1.6 | 38.0[a] | 41.5 ± 0.8 | 38.6[a] | ||||||||||||||
| With solar load, white hair | 34.8 ± 1.1 | 38.9 ± 0.7 | ||||||||||||||||
[a] Model results have no hair coat color characterization. | ||||||||||||||||||
Model respiration rates for the hot and humid treatment were 70 and 106 bpm without and with the solar load, respectively. For the hot and dry treatment, the corresponding model respiration rates were 84 and 118 bpm, respectively. All model respiration rates were within one standard deviation of the measured mean for both the hot and humid conditions and the hot and dry conditions (table 4). Well-modeled respiration rates demonstrate that the model represents how lactating cows respond to conditions in hot and humid and hot and dry conditions. Respiration rates are also commonly used by animal care personnel to assess the heat stress cows are experiencing.
Body Temperature
Gebremedhin et al. (2010) reported that the mean measured rectal temperatures for the hot and humid treatment were 38.8°C and 39.6°C, respectively, for the cases without and with a solar load. For the hot and dry treatment, the mean rectal temperatures were 39.4°C and 40.6°C for the without and with solar load cases, respectively. Rectal temperature standard deviations were 0.3°C and 0.6°C for the hot and humid treatment and 0.5°C and 0.4°C for the hot and dry treatments for the without and with solar load cases, respectively (Gebremedhin et al., 2010).
Model body temperatures for the hot and humid treatment were 39.3°C and 40.3°C without and with the solar load, respectively. For the hot and dry treatment, the corresponding model temperatures were 39.7°C and 40.6°C, respectively. Both model body temperatures for the hot and humid conditions were more than one standard deviation higher than the measured mean. For the hot and dry conditions, the model body temperatures were within one standard deviation of the measured mean body temperatures (table 4), which indicates that the model accuracy described the heat exchange and body temperature conditions for hot and dry conditions accurately.
Skin Temperature
Mean measured dorsal skin temperatures ranged from 34.8°C to 37.7°C for the hot and humid treatment and 36.5 °C to 41.5°C for the hot and dry treatment with and without the solar loads. The dorsal skin temperature standard deviation ranged from 0.7°C to 1.1°C across both the hot and humid conditions and the hot and dry conditions (Gebremedhin et al., 2010).
Model skin temperatures were 36.4°C and 38.0°C for the hot and humid treatment, and 37.0°C and 38.6°C for the hot and dry treatment with and without the solar load, respectively (table 4). Model skin temperature results were within one standard deviation of the mean for hot and dry conditions without a solar load and hot and humid with a solar load. The model skin temperature for hot and dry conditions with a solar load was below the measured mean by over one standard deviation. For the hot and humid conditions without a solar load, the model skin temperature was about 1.6 °C or double the standard deviation above the measured mean (table 4).
Chen et al. (2015) Results
Chen et al. (2015) reported a baseline body temperature for the 18 lactating cows of 39.2 ± 0.6°C (mean ± SD), baseline respiration rate of 88 ± 16.5 bpm, side skin temperature of 37.3 ± 0.8°C, shoulder skin temperature of 38.5 ± 1.1°C, upper leg skin temperature of 36.8 ± 1.0°C, and lower leg skin temperature was 36.4 ± 1.1°C. Figure 1 shows the baseline body, side skin, upper leg, and lower leg temperatures and standard deviations reported.
The model body temperature for the baseline conditions was 39.1°C, which was within 0.1°C of the reported measured baseline temperature of 39.2°C (fig. 1). Model respiration rate was 63 bpm, which was 25 bpm lower than the measured baseline 88 bpm respiration rate. Model skin temperature was 36.1°C, which was lower than all the measured baseline skin temperatures, ranging from 2.4°C lower than the baseline shoulder skin temperature to 0.3°C lower than the lower leg skin temperature (fig. 1). The model results indicate that the model described heat exchange and cow conditions accurately for the conditions reported by Chen et al. (2015).
 |
| Figure 1. Reported mean and standard deviation for baseline body, side skin, shoulder skin, upper leg skin, and lower leg skin temperatures based on Chen et al. (2015) and model body and model skin temperatures. |
Morris Results
The mean measured reticular temperatures for the ten cases listed in table 3 for cows on pasture standing, grazing, or walking in non-shaded paddocks are listed in table 5 with corresponding model body temperatures. Six measured reticular temperatures were averaged over one hour, and all standard deviations were 0.1°C or less, which was less than the reported bolus temperature accuracy (i.e., ± 0.25°C) and indicated steady-state temperatures in each cow’s reticulum.
Previous researchers have reported that the reticular temperature may not be the same as the core body temperature. Bewley et al. (2008) measured reticular and rectal temperatures simultaneously and reported that reticular temperatures were 0.45°C higher than rectal temperatures. Ammer et al. (2016) compared different body temperature measuring methods in lactating cows and observed that mean reticular temperatures were higher than rectal temperatures. Overall averaged reticular temperatures (38.5 ± 0.7°C) were 0.4°C higher than rectal temperatures (38.1 ± 0.4°C) (Ammer et al., 2016). This temperature difference means that the model temperature would be expected to be below the reported reticular temperature in table 5.
| Table 5. Average measured reticular temperatures, model body temperature, and adjusted reticular temperature results for Morris cases outlined in table 1. | ||||
| Case | Cow ID | Measured Reticular Temperature (°C) | Model Body Temperature (°C) | Adjusted Reticular Temperature (°C) |
| 1 | 1762 | 39.4 | 38.9 | 39.0 |
| 2 | 1762 | 39.3 | 38.7 | 38.9 |
| 3 | 1631 | 38.9 | 38.9 | 38.5 |
| 4 | 15103 | 39.1 | 38.8 | 38.7 |
| 5 | 15103 | 39.0 | 38.6 | 38.6 |
| 6 | 1513 | 39.0 | 38.7 | 38.6 |
| 7 | 1715 | 39.3 | 38.6 | 38.9 |
| 8 | 1715 | 39.5 | 38.2 | 39.1 |
| 9 | 15103 | 39.2 | 38.1 | 38.8 |
| 10 | 1631 | 39.1 | 38.1 | 38.7 |
In all cases, model body temperatures were below the mean measured reticular temperatures, ranging from 0.1°C to 1.3°C lower. The model body temperatures were closer, only 0.1°C to 0.7°C lower than the reticular temperatures for cases 1 through 7, when the ambient air temperatures were warmer (i.e., 24.4°C to 26.5°C), similar to the standard deviation for reticular temperatures (i.e., ± 0.7°C) reported by Ammer et al. (2016). For cases 8 through 10, when the air temperatures were between 20°C and 22°C, the model body temperatures were either 1.0°C or 1.3°C below the reticular temperatures.
If the reticular temperatures are reduced by 0.4°C based on Bewley et al. (2008) and Ammer et al. (2016), the model temperatures range from 0.3°C below to 0.1°C above the adjusted reticular temperatures (fig. 2 and table 5), for cases 1 through 7 when ambient temperatures were warmer (table 3). For the cooler weather cases, 8 through 10, the model temperatures were 0.6°C to 0.9°C below the adjusted reticular temperatures (fig. 2 and table 5), which is very close to the standard deviation value reported for measured reticular temperatures by Ammer et al. (2016).
 |
| Figure 2. Model body temperatures and adjusted reticular temperatures for ten cases of cows on pasture standing in sunshine during warm weather. |
Measured cow body temperatures, respiration rates, and sweating rates were found to vary across cows (Gebremedhin et al., 2010; Chen et al., 2015). The steady-state model results compared well with the measured values and were all within the ranges of all readings obtained. More research is needed to measure more model inputs and assumed coefficients to validate the model more fully. A dynamic model would need to be developed to model the cyclical sweating rate and skin temperatures observed by Gebremedhin et al. (2010).
Conclusion
The results from the steady-state process-based lactating cow thermal balance model developed by Nelson and Janni (in press) compared well with mean measured values from two published studies (Gebremedhin et al., 2010; Chen et al., 2015) and unpublished data collected as part of a solar shade study (Sharpe et al., 2021). The spreadsheet model results were commonly within one standard deviation of the reported means.
All model sweating rates, which ranged from 191 to 295 g m-2 h-1, were within one standard deviation (i.e., ± 90.7 to ± 159 g m-2 h-1) of the measured mean of high-producing multiparous Holstein cows exposed to both hot and humid conditions and hot and dry conditions studied by Gebremedhin et al. (2010). Similarly, all model respiration rates, which ranged from 70 to 118 bpm, were within one standard deviation of the measured mean respiration rates (i.e., ± 12.4 to ± 15.0 bpm) (Gebremedhin et al., 2010). Model body temperatures, which ranged between 39.3°C and 40.6°C, were within one or two standard deviations (i.e., ± 0.3°C to ± 0.6°C) of the mean measured body temperatures (Gebremedhin et al., 2010). Model skin temperatures ranged from within one to two standard deviations of the measured skin temperatures (Gebremedhin et al., 2010).
The model body temperature for the average baseline conditions was 39.1°C, which was within 0.1°C of the reported average baseline intravaginal body temperature of lactating, pregnant Holstein-Friesian cows studied by Chen et al. (2015). The model respiration rate was 25 bpm lower than the reported average baseline 88 bpm respiration rate (Chen et al., 2015). The model skin temperature, 36.1°C, ranged from 0.3°C to 2.4°C lower than all four baseline skin temperatures reported (Chen et al., 2015).
Model body temperatures for standing crossbred cows of a low-input grazing herd on pasture were 0.1°C to 0.7°C lower than measured mean reticular temperatures when the ambient air temperatures were between 24.4°C and 26.5°C. When air temperatures were between 20°C and 22°C, the model body temperatures were 1.0°C to 1.3°C below the reported mean reticular temperatures.
The model can be used to assess factors that lead to heat stress for lactating cows (e.g., body mass, milk yield, solar load, air dry-bulb temperature, dew-point temperature, and air velocity) and practices to mitigate heat stress (e.g., air velocity and shade).
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