Figure 1.
Example of image analysis histograms of frequency of occurrences of different gray pixel values as an indicator of brightness. Each histogram represents pixels selected for (A) snow, (B) a white cow, (C) a red cow, and (D) a black cow, concurrently in a photo. Photos were taken in January 2016 west of Laramie, WY, USA at the University of Wyoming, Agricultural Experiment Station, Laramie Research and Extension Center—Beef Unit and cattle were Bos taurus cows. Analyses were conducted using open-source image analysis software ImageJ.
Figure 1.
Example of image analysis histograms of frequency of occurrences of different gray pixel values as an indicator of brightness. Each histogram represents pixels selected for (A) snow, (B) a white cow, (C) a red cow, and (D) a black cow, concurrently in a photo. Photos were taken in January 2016 west of Laramie, WY, USA at the University of Wyoming, Agricultural Experiment Station, Laramie Research and Extension Center—Beef Unit and cattle were Bos taurus cows. Analyses were conducted using open-source image analysis software ImageJ.
Figure 2.
Field method for in situ measurement of ambient environmental temperature (Tempamb) and cattle surface temperature (Tempcow) using two separate thermal instruments simultaneously operated by a single technician. Tempamb measured with a handheld meter (HHM; Kestrel® 3000). Tempcow measured with an infrared gun (IRG) high temperature thermometer (Extech Instruments® 42,545 made by FLIR Systems®) with the laser placed approximately at the top of the shoulder from a distance of 5 to 15 m and sensed temperature was recorded. Tempamb and Tempcow were recorded simultaneously with HHM and IRG instruments in the same physical position. Cattle were white, red, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agricultural Experiment Station, Laramie Research and Extension Center—Beef Unit.
Figure 2.
Field method for in situ measurement of ambient environmental temperature (Tempamb) and cattle surface temperature (Tempcow) using two separate thermal instruments simultaneously operated by a single technician. Tempamb measured with a handheld meter (HHM; Kestrel® 3000). Tempcow measured with an infrared gun (IRG) high temperature thermometer (Extech Instruments® 42,545 made by FLIR Systems®) with the laser placed approximately at the top of the shoulder from a distance of 5 to 15 m and sensed temperature was recorded. Tempamb and Tempcow were recorded simultaneously with HHM and IRG instruments in the same physical position. Cattle were white, red, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agricultural Experiment Station, Laramie Research and Extension Center—Beef Unit.
Figure 3.
Examples of in situ measurement of ambient environmental temperature (Tempamb) and cattle surface temperature (Tempcow) using a handheld meter (HHM; Kestrel® 3000) and an infrared gun (IRG) high temperature thermometer (Extech Instruments® 42,545 made by FLIR Systems®). Temperatures collected from animals and the environment in situ were then used to calculate the difference (ΔT) between Tempcow and Tempamb. Cattle were white, red, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station, Laramie Research and Extension Center—Beef Unit.
Figure 3.
Examples of in situ measurement of ambient environmental temperature (Tempamb) and cattle surface temperature (Tempcow) using a handheld meter (HHM; Kestrel® 3000) and an infrared gun (IRG) high temperature thermometer (Extech Instruments® 42,545 made by FLIR Systems®). Temperatures collected from animals and the environment in situ were then used to calculate the difference (ΔT) between Tempcow and Tempamb. Cattle were white, red, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station, Laramie Research and Extension Center—Beef Unit.
Figure 4.
Winter albedo values for white, red, and black cows. Albedo values derived from pixel analyses with snow albedo as a reference. Data were transformed with an arcsine transformation and then analyzed with a non-parametric Kruskal–Wallis test with hide color as the fixed effect. Cohen’s d effect sizes were calculated to understand the magnitude of differences based on the defined alternative hypotheses (HA) for each paired comparison; specifically, HA1: white cow albedo > red cow albedo, HA2: red cow albedo > black cow albedo, and HA3: white cow albedo > black cow albedo. Significant statistical differences were based on α = 0.05 (and indicated by different letters; (a–c)). Cattle were red, white, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station, Laramie Research and Extension Center—Beef Unit.
Figure 4.
Winter albedo values for white, red, and black cows. Albedo values derived from pixel analyses with snow albedo as a reference. Data were transformed with an arcsine transformation and then analyzed with a non-parametric Kruskal–Wallis test with hide color as the fixed effect. Cohen’s d effect sizes were calculated to understand the magnitude of differences based on the defined alternative hypotheses (HA) for each paired comparison; specifically, HA1: white cow albedo > red cow albedo, HA2: red cow albedo > black cow albedo, and HA3: white cow albedo > black cow albedo. Significant statistical differences were based on α = 0.05 (and indicated by different letters; (a–c)). Cattle were red, white, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station, Laramie Research and Extension Center—Beef Unit.
Figure 5.
Linear least-squares regression to analyze how ambient environmental temperature (Tempamb) predicts ΔT (the difference between cattle surface temperature (Tempcow) and Tempamb) stratified by cow hide color for white, red, and black cows. Strength of relationships was determined based on the correlation coefficient (r2) and significant statistical differences based on α = 0.05. Cattle were red, white, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station, Laramie Research and Extension Center—Beef Unit. Dashed lines represent 95% prediction bands.
Figure 5.
Linear least-squares regression to analyze how ambient environmental temperature (Tempamb) predicts ΔT (the difference between cattle surface temperature (Tempcow) and Tempamb) stratified by cow hide color for white, red, and black cows. Strength of relationships was determined based on the correlation coefficient (r2) and significant statistical differences based on α = 0.05. Cattle were red, white, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station, Laramie Research and Extension Center—Beef Unit. Dashed lines represent 95% prediction bands.
Table 1.
Potential predictor variables and associated justification for inclusion for modeling external surface temperatures of red, white, and black hided cattle (Tempcow) and then the difference (ΔT) between Tempcow and the ambient temperature of the surrounding environment (Tempamb). Variables are listed in alphabetical order. Cattle were white, red, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station—Beef Unit.
Table 1.
Potential predictor variables and associated justification for inclusion for modeling external surface temperatures of red, white, and black hided cattle (Tempcow) and then the difference (ΔT) between Tempcow and the ambient temperature of the surrounding environment (Tempamb). Variables are listed in alphabetical order. Cattle were white, red, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station—Beef Unit.
Variable | Biological Rationale and Justification for Inclusion in Modeling |
---|
Ambient environmental temperature (Tempamb) a | Also noted as air temperature, this is important to determine an organism’s deviation from the zone of thermoneutrality and influences convection coefficients [27]. |
Clear sky insolation index (KTClear) d | Used for the weather prediction of intra-day solar forecasting [28] and for daylight utilization in farm animal production [29]. Fraction of insolation available at the top of the atmosphere and an indication of the total solar radiation incident on a horizontal earth surface. |
Cow winter albedo 1,a | Commonly used in remote sensing research, this refers to the proportion of solar radiation reflected by any surface (water, land, organismal), where darker surfaces reflect less than lighter surfaces and is important for determining energy balance [30]. Measured in winter when snow was available to relativize pixel brightness in images. |
Cow surface temperature (Tempcow) a | The surface temperature of an organism can be used to predict convective heat loss [27]. |
Dewpoint temperature (Tempdew) c | The temperature to which air must be cooled, relative to pressure and water-vapor content, in order to reach saturation and for dew or condensation to form; this influences evaporative heat loss [31]. |
Earth skin temperature (Tempearth) d | The earth’s surface temperature as opposed to the meteorological definition of surface temperature which is actually measured by suspended air thermometers above the surface of the earth; this reflects the thermal environments of physiologically diverse organisms [32]. |
Humidity b | The amount of water vapor that is in the atmosphere; humidity interacts with temperature and influences thermal stress of animals [33]. Humidity is also important given the temperature–humidity index (THI) which can have a combined interactive impact [3]. |
Long-wave radiation (infrared; RadLW) d | Downward thermal infrared long-wave radiative flux d; has an important role in predicting radiative heat gain for animals with different hide colors, particularly at the surface of the animal [34]; may govern simulated temperatures of wildlife species [35]. |
Short-wave radiation (visible; RadSW) d | dAll sky insolation incident on a horizontal surface (short-wave) d; short-wave solar radiation has been used to develop a thermal stress index for dairy cows in Brazil [9]. |
Vapor pressure deficit (VPD) c | The difference between the amount of moisture in the air and the maximum moisture the air can hold at saturation; this affects the exchange of the energy between an animal and its environment through an interaction with temperature [36,37]. |
Wind speed b | Also noted as wind flow speed, this is a basic atmospheric measurement of air moving from high to low pressure often driven by temperature flux. This variable is considered in the calculation of the convection coefficient and an influential for predicting the surface temperature of an organism [36]. |
Table 2.
Units, means, minimums, and maximums of potential predictor variables and associated justification for inclusion for modeling external surface temperatures of red, white, and black hided cattle (Tempcow) and then the difference (ΔT) between Tempcow and the ambient temperature of the surrounding environment (Tempamb). Variables are listed in alphabetical order. Cattle were white, red, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station, Laramie Research and Extension Center—Beef Unit.
Table 2.
Units, means, minimums, and maximums of potential predictor variables and associated justification for inclusion for modeling external surface temperatures of red, white, and black hided cattle (Tempcow) and then the difference (ΔT) between Tempcow and the ambient temperature of the surrounding environment (Tempamb). Variables are listed in alphabetical order. Cattle were white, red, and black Bos taurus cows free roaming on rangeland west of Laramie, WY, USA at the University of Wyoming, Agriculture Experiment Station, Laramie Research and Extension Center—Beef Unit.
Variable | Unit | Mean | Minimum | Maximum |
---|
Ambient environmental temperature (Tempamb) | °C | 4.4 | −32.8 | 35.6 |
Clear sky insolation index (KTClear) | unitless index; 0–1 | 0.6 | 0.3 | 0.8 |
Cow winter albedo | unitless index; 0–255 | 0.25 | 0.04 (black cows) | 0.69 (white cows) |
Cow surface temperature (Tempcow) | °C | 32.4 | −10.7 | 63.1 |
Dewpoint temperature (Tempdew) | °C | −10.0 | −27.6 | 7.1 |
Earth skin temperature (Tempearth) | °C | −0.1 | −24.6 | 23.0 |
Humidity | % | 56.7 | 9.0 | 84.0 |
Long-wave radiation (infrared; RadLW) | kW hr per m2 per day | 5.9 | 3.6 | 8.7 |
Short-wave radiation (visible; RadSW) | kW hr per m2 per day | 3.9 | 1.3 | 8.5 |
Vapor pressure deficit (VPD maximum) | hPa | 13.5 | 0.6 | 32.5 |
Wind speed | km/h | 29.0 | 11.3 | 53.1 |
Table 3.
Weather, radiation, and cow albedo models assessed for cow surface temperature (Tempcow) for white, red, and black Bos taurus cows near Laramie, WY, USA.
Table 3.
Weather, radiation, and cow albedo models assessed for cow surface temperature (Tempcow) for white, red, and black Bos taurus cows near Laramie, WY, USA.
Model | K | AICc | ΔAICc | ωi |
---|
Step 1—Weather Models |
Ambient Temperature (Tempamb) | 3 | 4967.08 | 0.00 | 1 |
Dewpoint Temperature (Tempdew) | 3 | 4980.38 | 13.30 | 0 |
Wind Speed | 3 | 5023.33 | 56.25 | 0 |
Null | 2 | 5023.93 | 56.85 | 0 |
Step 2—Radiation Models |
Clear Sky Insolation (KTClear) | 3 | 4988.16 | 0.00 | 0.97 |
Long-wave Radiation (RadLW) | 3 | 4995.78 | 7.62 | 0.02 |
Short-wave Radiation (RadSW) | 3 | 4998.08 | 9.92 | 0.01 |
Null | 2 | 5023.93 | 35.77 | 0.00 |
Step 3—Top Models + Winter Albedo |
Tempamb + KTClear + Albedo | 5 | 4674.57 | 0.00 | 1 |
Tempamb + KTClear | 4 | 4959.79 | 285.22 | 0 |
Tempamb | 3 | 4967.08 | 292.51 | 0 |
KTClear | 3 | 4988.16 | 313.58 | 0 |
Null | 2 | 5023.93 | 349.35 | 0 |
Table 4.
Top candidate model parameter estimates and 95% confidence intervals for cow surface temperature (Tempcow) for white, red, and black Bos taurus cows near Laramie, WY, USA.
Table 4.
Top candidate model parameter estimates and 95% confidence intervals for cow surface temperature (Tempcow) for white, red, and black Bos taurus cows near Laramie, WY, USA.
Variable | Estimate | Lower | Upper |
---|
Ambient Temperature (Tempamb) | 0.1770 | 0.1328 | 0.2213 |
Clear Sky Insolation (KTClear) | 19.172 | 13.1404 | 25.2043 |
Albedo | −27.026 | −29.8800 | −24.1729 |
Table 5.
Weather, radiation, and cow albedo models assessed for the difference (ΔT) between external surface temperatures of cattle (Tempcow) and the ambient temperature of the surrounding environment (Tempamb) for white, red, and black Bos taurus cows near Laramie, WY, USA.
Table 5.
Weather, radiation, and cow albedo models assessed for the difference (ΔT) between external surface temperatures of cattle (Tempcow) and the ambient temperature of the surrounding environment (Tempamb) for white, red, and black Bos taurus cows near Laramie, WY, USA.
Model | K | AICc | Delta AICc | Weight |
---|
Step 1—Weather Models |
Ambient Temperature (Tempamb) | 3 | 4967.08 | 0.00 | 1 |
Dewpoint Temperature (Tempdew) | 3 | 5184.00 | 216.92 | 0 |
Wind Speed | 3 | 5540.83 | 573.75 | 0 |
Null | 2 | 5684.51 | 717.43 | 0 |
Step 2—Radiation Models |
Long-wave Radiation (RadLW) | 3 | 5142.32 | 0.00 | 1 |
Short-wave Radiation (RadSW) | 3 | 5258.25 | 115.93 | 0 |
Clear Sky Insolation (KTClear) | 3 | 5616.83 | 474.51 | 0 |
Null | 2 | 5684.51 | 542.19 | 0 |
Step 3—Top Models + Animal Attributes [Winter Albedo and Tempcow] |
Tempamb + RadLW + Albedo + Tempcow | 6 | −38,308.95 | 0.00 | 1 |
Tempamb + RadLW + Tempcow | 5 | −38,197.42 | 111.53 | 0 |
Tempamb + RadLW + Albedo | 5 | 4674.41 | 42,983.36 | 0 |
Tempamb + RadLW | 4 | 4961.41 | 43,270.42 | 0 |
RadLW | 3 | 5142.32 | 43,451.27 | 0 |
Tempamb | 3 | 4967.08 | 43,276.03 | 0 |
Null | 2 | 5684.51 | 43,993.46 | 0 |
Table 6.
Top candidate model parameter estimates and 95% confidence intervals for the difference (ΔT) between external surface temperatures of cattle (Tempcow) and the ambient temperature of the surrounding environment (Tempamb) for white, red, and black Bos taurus cows near Laramie, WY, USA.
Table 6.
Top candidate model parameter estimates and 95% confidence intervals for the difference (ΔT) between external surface temperatures of cattle (Tempcow) and the ambient temperature of the surrounding environment (Tempamb) for white, red, and black Bos taurus cows near Laramie, WY, USA.
Variable | Estimate | Lower | Upper |
---|
Ambient Temperature (Tempamb) | −0.8230 | −0.8672 | −0.7787 |
Long-wave radiation (RadLW) | −8.3971 | −8.9595 | −7.8347 |
Albedo | −24.160 | −29.8022 | −18.5184 |
Cow Surface Temperature (Tempcow) | 0.5022 | 0.37772 | 0.62661 |