# Temperature–Humidity-Dependent Wind Effects on Physiological Heat Strain of Moderately Exercising Individuals Reproduced by the Universal Thermal Climate Index (UTCI)

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## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

#### 1.1. Sustainable Heat Stress Mitigation by Wind

^{2}), whereas physical loads at workplaces and many home and outdoor activities are associated with metabolic rates higher than 2 MET [22,23].

_{a}= 0.3 m/s) under warm–humid conditions (Figure 1a) may be explained by hidromeiosis [26], which did not occur when increasing the wind speed to v

_{a}= 2.0 m/s enhanced sweat evaporation [27]. On the other hand, under hot–dry conditions (Figure 1b), the already high level of evaporative efficiency could not be further elevated by increased airflow and thus could not compensate for the higher convective heat gain aggravating physiological strain, in particular rising sweat rates [28].

#### 1.2. Study Objectives

## 2. Materials and Methods

#### 2.1. Experimental Data

**RefWind**, with air velocity v

_{a}= 0.3 m/s) and high wind (

**HiWind**, v

_{a}= 2 m/s) conditions. Here, 2 m/s constituted the maximum value of controllable wind speed in the climatic chamber, corresponding to average airflow conditions observable in (semi-)outdoor workplaces and in coal mines [24]. Inclusion criteria were a minimum number of 15 experiments per series with comparable workloads and clothing. We retrieved 198 trials organized in 10 series, which originated from five acclimated, semi-nude (basic clothing insulation I

_{cl}= 0.1 clo, 1 clo = 0.155 K·m

^{2}·W

^{−1}), young, and fit males under RefWind and HiWind conditions, respectively. The number of experiments in each series varied inter-individually and depended on wind conditions between 16 and 25 experiments, with total numbers of 97 trials for RefWind and 101 for HiWind. The average personal characteristics (mean ± SD, with range in brackets) of the five participants were 20.1 ± 0.9 (19–22) years of age, 1.87 ± 0.02 (1.84–1.88) m of body height, 70.5 ± 2.1 (68–73) kg of body weight, 1.94 ± 0.02 (1.92–1.97) m

^{2}of body surface area, and 47.9 ± 6.4 (43.2–57.4) mL/min/kg of maximal oxygen consumption. Before exposure, the participants had undergone a heat acclimation protocol lasting at least three weeks [43].

_{a}; range 25–55 °C) and humidity, expressed as water vapor pressure (p

_{a}; 0.5–5.3 kPa). Mean radiant temperature (T

_{mrt}) was equal to T

_{a}. Trials were stopped prematurely if rectal temperature exceeded 38.5 °C or on the participant’s demand.

_{re}) were recorded continuously using a thermistor probe (YSI 401, YSI Inc., Yellow Springs, OH, USA) inserted 10 cm past the anal sphincter. Local skin temperatures were measured with thermistors (YSI 427, YSI Inc., Yellow Springs, OH, USA) at the forehead (T

_{sk,head}), chest (T

_{sk,chest}), back (T

_{sk,back}), upper arm (T

_{sk,arm}), thigh (T

_{sk,thigh}), and lower leg (T

_{sk,leg}), and were used to calculate mean skin temperature (T

_{sk}) as weighted average of the local skin temperatures according to [24], shown in Equation (1):

_{sk}= 0.05 × T

_{sk,head}+ 0.2 × T

_{sk,chest}+ 0.15 × T

_{sk,back}+ 0.2 × T

_{sk,arm}+ 0.25 × T

_{sk,thigh}+ 0.15 × T

_{sk,leg}

_{re}and T

_{sk}. As illustrated by the yellow shaded areas in Figure 1, the averages of T

_{re}, HR, T

_{sk}, and SR over the third hour of exposure, representing steady-state [25], were submitted to the following data analysis.

#### 2.2. Data Analysis and Statistics

_{ij}] = µ + s(ID

_{i}) + te(T

_{a,ij}, p

_{a,ij}) + te

_{Δv}(T

_{a,ij}, p

_{a,ij}) + ε

_{ij}

_{re}, T

_{sk}, and SR, respectively, as responses from experiment j of participant i (Y

_{ij}) by separate GAMs. These models included an overall intercept µ, and a bivariate penalized tensor regression spline te(T

_{a,ij}, p

_{a,ij}) for the effects of air temperature and humidity depending on the (T

_{a}, p

_{a}) combinations, accounting for the repeated measurements by subject-specific intercepts as random coefficients s(ID

_{i}) [46]. Adding another bivariate spline te

_{Δv}(T

_{a,ij}, p

_{a,ij}) as so-called factor smooth interaction [44] of the regression splines with the wind condition (RefWind vs. HiWind), we obtained estimates for the wind effect Δ

_{v}, i.e., the response difference under HiWind compared to RefWind over the (T

_{a}, p

_{a}) grid supplemented by p-values [47]. These were then visualized in a difference plot [48].

_{i}) refers to a cubic regression spline with basis dimension (or rank) set to k = 5 (i.e., with k − 1 = 4 as upper limit of the associated degrees of freedom). Similarly, te(T

_{a,ij}, p

_{a,ij}) and te

_{Δv}(T

_{a,ij}, p

_{a,ij}) represent tensor products of two cubic regression spline bases for the T

_{a}and p

_{a}dimension, respectively, each of rank k = 9, and are hence of total rank k = 81. Maximum likelihood parameter estimates with standard errors and p-values were obtained assuming Gaussian error ϵ

_{ij}[47]. Calculations were performed with the R software version 4.2.1 [49] using the package mgcv [44] together with mgcViz [48] and tidymv [50].

#### 2.3. UTCI Calculations

_{a}), ambient water vapor pressure (p

_{a}), mean radiant temperature (T

_{mrt}), and air velocity 10 m above ground (v

_{a,10m}).

#### 2.3.1. UTCI Sensitivity to Wind

_{a,10m}). For conversion to any other measurement height, e.g., 1 m for person level, the operational procedure [39] provides a logarithmic formula, shown in Equation (3), indicating that air velocity at person level (v

_{a,1m}) is computed as the 10 m value (v

_{a,10m}) divided by 1.5, in accordance with international standards [51].

_{a,1m}= v

_{a,10m}× log(1/0.01)/log(10/0.01) = v

_{a,10m}/1.5

_{w}= 1.1 m/s, this is taken into account by calculating the resulting or relative air velocity at person level (v

_{ar,1m}), according to Equation (4). Here, α denotes the angle between the directions of walking and wind assigned to zero for indicating the same direction. As UTCI does not assume a specific angle, v

_{ar,1m}is calculated by integrating Equation (4) over all α between zero and 2π [34,52].

_{ar,1m}used by UTCI for calculating the convective and evaporative heat loss [33]. Notably, reducing wind speed below v

_{a,10m}= 0.5 m/s (v

_{a,1m}= 0.3 m/s) will hardly impact v

_{ar,1m}, which is limited by v

_{w}, while v

_{ar,1m}will approach v

_{a,1m}for v

_{a,10m}above 3 m/s.

#### 2.3.2. Wind Effect on UTCI

_{a,10m}on UTCI (Δ

_{v}UTCI) compared to the reference wind speed (v

_{a,10m,ref}= 0.5 m/s) while keeping the other parameters constant, as shown in Equation (5):

_{v}UTCI = UTCI(T

_{a};p

_{a};v

_{a,10m};T

_{mrt}) − UTCI(T

_{a};p

_{a};v

_{a,10m,ref};T

_{mrt})

_{v}UTCI for combinations of T

_{a}between 25 and 50 °C and of p

_{a}from 0.1 to 5 kPa with relative humidity of rH ≤ 100% while setting T

_{mrt}= T

_{a}, as in the experiments. We performed the calculations for the reference wind speed (v

_{a,10m,ref}= 0.5 m/s), matching RefWind with v

_{a,1m}= 0.3 m/s (Figure 2), and increased wind speeds with v

_{a,10m}= 3 m/s, matching HiWind with v

_{a,1m}= 2 m/s.

_{mrt}= T

_{mrt}−T

_{a}from 0 to 30 K in steps of 10 K. In addition, we considered conditions with higher wind speeds of v

_{a,10m}= 4 and 6 m/s, respectively. Here, v

_{a,10m}= 4 m/s corresponds to an increase of 1.7 m/s in relative air velocity at body level (v

_{ar,1m}), according to Figure 2, matching the settings of the climate chamber experiments, whereas v

_{a,10m}= 6 m/s (v

_{a,1m}= 4 m/s) parallels the wind speed applied in several simulations and experimental studies [15,17,18,19,20,28].

#### 2.3.3. UTCI Prediction of Physiological Wind Effects

_{v}UTCI with the wind effects obtained for the physiological variables by scatterplots, including Spearman correlation coefficients (r

_{s}). In addition, we quantified the predictive performance of UTCI in the binary classification of the occasion of heating wind effects (Δ

_{v}> 0) on physiological variables by calculating the sensitivity, specificity, and overall accuracy.

## 3. Results

#### 3.1. Wind Effects Assessed by UTCI

_{v}UTCI = 0.

_{v}UTCI depending on the temperature and humidity. Wind cooling (blueish) increased with a decreasing temperature and increasing humidity, while heating due to wind (reddish) increased with an increasing temperature and decreasing humidity.

#### 3.2. Wind Effects on Physiological Heat Strain

_{re}were complete, there were a few missing values for HR, T

_{sk}, and SR. The estimated mean values of 103 bpm (HR), 37.6 °C (T

_{re}), 35.5 °C (T

_{sk}), and 744 g/h (SR), respectively, were typical for light to moderate activities under heat stress [24,38]. The goodness-of-fit was good to excellent, with more than three quarters of the variance explained (R

^{2}> 75%) and small residual standard errors for HR, T

_{re}, and T

_{sk}. SR showed almost a 90% explained variance but a slightly increased standard error, which, however, was still below 125 g/h, considered the relevant accuracy limit acceptable in occupational or military settings [54]. Moreover, graphical model checking, as displayed in Appendix A in Figure A2, did not reveal any problematic issues concerning the underlying model assumptions.

_{a}, p

_{a}) modeling the influence of temperature and humidity were statistically highly significant (p < 0.0001). Similarly, the moderating effects of wind speed, as considered by the bivariate interaction splines te

_{Δv}(T

_{a}, p

_{a}), were statistically significant for HR, T

_{re}, T

_{sk}, and SR.

_{re}, T

_{sk}, and SR, respectively, whereas individual influences on HR appeared to be less pronounced (p = 0.20).

_{re}, T

_{sk}, and SR. Although the shape of the lines varied between the four variables and additionally depended on the strain level, a general pattern emerged, with contours bended upward to the left indicating strain levels increasing with temperature and humidity, as had also occurred for UTCI (Figure 3a). Again, similar to the UTCI, the dashed lines (HiWind) were above the solid lines (RefWind) at low temperatures and under hot–humid conditions, demonstrating reduced strain due to wind cooling, whereas in hot–dry climates, the opposite was found, with solid lines above dashed lines indicating higher strain levels with increased wind speed.

_{v}= 0, thus demonstrating that the threshold separating cooling from heating effects was bended upward to the right, resemblingthe UTCI (Figure 3b), but with a greater curvature. They indicated reduced heat strain with HiWind at low temperatures and in hot–humid conditions, with limiting vapor pressure above 2 kPa for HR and T

_{re}and above 3 kPa for T

_{sk}and SR, respectively.

_{v}= 0.

_{sk}, and SR were found under hot–arid conditions with a temperature above 40 °C and vapor pressure below 1 kPa. Temperatures below 35 °C yielded no detrimental wind effects.

_{re}only appeared for very humid conditions with vapor pressures approaching 4 kPa.

#### 3.3. UTCI Assessment Related to Physiological Wind Effects

_{v}) on the UTCI with the physiological effects show positive correlations with the closest agreement (r ≈ 0.9) for skin temperature and sweat rate, also concerning the transition from cooling (Δ

_{v}< 0) to heating (Δ

_{v}> 0) effects. Slightly lower correlations were observed with the effects on heart rates and core temperature.

_{sk}and SR.

_{re}.

_{v}> 0) as sensitivity, specificity, and accuracy in Figure 6b, these falsely predicted heating events resulted in lowered specificity and overall accuracy regarding HR and T

_{re}, whereas well-balanced figures emerged for T

_{sk}and SR.

#### 3.4. UTCI Assessment with Higher Wind Speeds and Thermal Radiation

_{v}) on the UTCI over the temperature–humidity grid for the different wind speeds and radiant heat loads, expressed as ΔT

_{mrt}= T

_{mrt}– T

_{a}, with the upper left panel with v

_{a,10m}= 3 m/s and ΔT

_{mrt}= 0 K repeating the data from Figure 3b. Figure 7 summarizes the wind effects Δ

_{v}UTCI depending on the wind speed and radiant heat load as boxplots calculated over the temperature–humidity grid.

_{v}UTCI < 0) and heating effects (Δ

_{v}UTCI > 0) at the extremes, as indicated by the minima and maxima, but also the first and third quartiles in Figure 7. In addition, the threshold line for Δ

_{v}UTCI = 0 slightly shifted toward higher temperatures for higher wind speeds (Figure A3), thus contributing to the decreasing trend with wind speed observed for the median effect in Figure 7.

_{v}UTCI, all percentiles showed a decreasing trend with an increasing radiant heat load ΔT

_{mrt}(Figure 7). The reduced reddish surface areas with an increased radiant heat load in Figure A3 suggest that this was attributable to a massive shift in the threshold line toward higher temperatures. Thus, wind-cooling effects occurred for a higher portion of climatic conditions over the temperature–humidity grid, shifting the Δ

_{v}UTCI distribution toward more negative values (Figure 7).

_{v}UTCI at v

_{a,10m}= 4 m/s (with ΔT

_{mrt}= 0 K) corresponded to the effect of increasing relative air velocity (v

_{ar,1m}) by 1.7 m/s (Figure 2), conforming to the change in the (relative) air velocity realized in the experiments. As the relevant UTCI calculations of convective and evaporative heat losses depend on the relative air velocity [33], we repeated the correlational analyses from Figure 6 for this condition, as shown in Figure A4. The outcome was very similar as before in Figure 6, though we observed slightly lowered correlations of the physiological wind effects with Δ

_{v}UTCI.

## 4. Discussion

#### 4.1. Temperature-Humdity-Dependent Wind Effect Thresholds

_{v}< 0) to heating (Δ

_{v}> 0) wind effects on physiological heat strain based on the experimental data. This is a distinguishing feature and particular strength of our study because corresponding experiments with sedentary participants have been limited to a few selected climatic conditions [15,16], so mapping the wind effect thresholds in relation to air temperature and humidity for low-active persons had to rely on simulation studies [17,18,19,20]. Recently, a study with exercising participants [28] aimed at the interaction of wind with combinations of temperature and humidity over a likewise extensive grid but focused on the physical work capacity with cardiac strain clamped at 130 bpm HR.

_{v}< 0) to heating (Δ

_{v}> 0) wind effects on skin temperatures and sweat rates. The UTCI’s assessment was more conservative, i.e., overpredictive, concerning the potential hazards due to additional heating by wind with respect to core temperature and heart rates (Figure 6b).

_{mrt}[36]. On the other hand, the limit of beneficial wind cooling was shifted toward higher temperatures, counteracting, at least partly, the heat gained from the increased radiant heat load. Similar interaction effects with wind decreasing the heat gain from radiant heat have been reported from thermal manikin measurements with work clothes [59,60]. However, as our results concerning the effects of heat radiation are purely modeled outcomes using UTCI, further supporting experimental studies with human participants concerning the interaction of wind with radiant heat load are required.

#### 4.2. Limitations and Outlook

_{cl}= 0.1 clo) might differ from the effects with clothed humans, e.g., as assumed by the UTCI with clothing insulation not falling below I

_{cl}= 0.3 clo [34]. On the other hand, prior studies with sedentary participants [15,16] applied similar minimal clothing settings. In addition, limited differences were found concerning the wind effects on the physical work capacity with minimal clothing compared to light and covering clothing [28], and the corresponding temperature–humidity charts in that study were produced for a person wearing I

_{cl}= 0.28 clo.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

- An additional example of recordings of physiological heat strain variables depending on temperature, humidity, and air velocity;
- Goodness-of-fit plots for the GAMs fitted to the physiological heat strain variables;
- Influence of radiant heat and wind speed on wind effects assessed by UTCI (Δ
_{v}UTCI); - Correlations between the wind effects of the physiological heat strain variables and UTCI calculated for v
_{a,10m}= 4 m/s.

**Figure A1.**Time course of heart rate (HR), rectal (T

_{re}) and mean skin temperature (T

_{sk}), and sweat rate (SR) of an acclimated participant during experiments in a hot−humid climate (

**a**) or in a hot−dry climate (

**b**) under both reference (v

_{a}= 0.3 m/s, red lines) and high air velocity (v

_{a}= 2 m/s, blue lines) conditions. The yellow shaded area marks the time interval with averaged values used for analyses. Note that the reference wind trial in (

**a**) was prematurely aborted in the 8th working period.

**Figure A2.**Diagnostic goodness−of−fit plots for the generalized additive models (GAMs) fitted to (

**A**) heart rate (bpm), (

**B**) rectal temperature (°C), (

**C**) mean skin temperature (°C), and (

**D**) sweat rate (g/h), respectively. The subplots show Q−Q plots of standardized residuals vs. the theoretical Gaussian quantiles (upper left panels), histograms of residual distribution (upper right), residuals vs. predicted values (lower left), and correlation of observed to fitted values (lower right).

**Figure A3.**Effect of radiant heat and wind speed on wind effects assessed by UTCI. Change in UTCI at increased wind speeds (Δ

_{v}UTCI) compared to the reference wind condition (v

_{a,10m}= 0.5 m/s) depending on air temperature and vapor pressure considering the influence of radiant heat load (ΔT

_{mrt}= T

_{mrt}− T

_{a}). Note that the upper left plot replicates the data of Figure 3b.

**Figure A4.**Correlation of wind effects from Figure 5 for heart rate (Δ

_{v}HR), rectal temperature (Δ

_{v}T

_{re}), mean skin temperature (Δ

_{v}T

_{sk}), and sweat rate (Δ

_{v}SR), respectively, with the wind effect on UTCI (Δ

_{v}UTCI) calculated for an elevated wind speed (4 m/s).

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**Figure 1.**Time course of heart rate (HR), rectal (T

_{re}) and mean skin temperature (T

_{sk}), and sweat rate (SR) of an acclimated participant during experiments in a hot–humid climate (

**a**) or in a hot–dry climate (

**b**) under both reference (v

_{a}= 0.3 m/s, red lines) and high air velocity (v

_{a}= 2 m/s, blue lines) conditions. The yellow shaded area marks the time interval with averaged values used for analyses. Note that the reference wind trial in (

**a**) was prematurely aborted in the 8th working period.

**Figure 2.**Relative wind speed at person level (v

_{ar,1m}) when moving with the UTCI reference walking speed (v

_{w}) of 4 km/h, corresponding to 1.1 m/s, in relation to wind speed measured at person level (v

_{a,1m}) and 10 m above ground (v

_{a,10m}). The insert provides a detailed view of the gray-shaded region for v

_{a,10m}≤ 4 m/s. Figures include solid lines of identity, and horizontal dashed lines indicating walking speed (v

_{w}).

**Figure 3.**Psychrometric charts showing (

**a**) UTCI contours related to air temperature and humidity (vapor pressure) representing the upper limits of ‘no thermal stress’ (UTCI = 26 °C), and ‘moderate’ (32 °C), ‘strong’ (38 °C), and ‘very strong’ (46 °C) heat stress, as well as an illustrative value for ‘extreme heat stress’ (55 °C), respectively. The influence of increased wind speed (HiWind with v

_{a,10m}= 3 m/s, corresponding to v

_{a,1m}= 2 m/s: dashed lines) is compared to the reference RefWind (v

_{a,10m}= 0.5 m/s, corresponding to v

_{a,1m}= 0.3 m/s: solid lines). The dot−dashed line connecting the intersections of RefWind with HiWind contours represents zero wind effects (Δ

_{v}= 0). This line is redrawn in (

**b**) as white contour together with the colored regions, indicating temperature–humidity combinations with cooling (blueish) or heating (reddish) wind effects on UTCI (Δ

_{v}UTCI), according to Equation (5), respectively, where color intensity indicates magnitude. Gray contours mark relative humidity (rH) levels. All values were calculated without additional radiant heat load (ΔT

_{mrt}= T

_{mrt}− T

_{a}= 0 K).

**Figure 4.**Psychrometric charts including contour lines with colors indicating separate levels of predicted values fitted by GAMs to (

**a**) heart rates (HR), (

**b**) rectal temperatures (T

_{re}), (

**c**) mean skin temperatures (T

_{sk}), and (

**d**) sweat rates (SR) in relation to air temperature and vapor pressure under RefWind (solid lines) and HiWind conditions (dashed lines), respectively. Dot-dashed lines connecting the intersections of RefWind with HiWind contours indicate zero wind effects (Δ

_{v}= 0).

**Figure 5.**Difference plots with contours of the wind effects (Δ

_{V}) estimated by GAMs in relation to air temperature and vapor pressure for (

**a**) heart rates (HR), (

**b**) rectal temperatures (T

_{re}), (

**c**) mean skin temperatures (T

_{sk}), and (

**d**) sweat rates (SR). White areas indicate temperature−humidity regions with non−significant wind effects (p > 0.05 testing for Δ

_{v}= 0 vs. Δ

_{v}≠ 0), the blueish areas mark significant reductions in physiological strain by wind cooling, while reddish areas depict significantly increased strain levels due to heating wind effects, respectively. Dashed lines show relative humidity levels, and the gray shaded areas indicate combinations not supported by data. Experimental conditions are marked by ‘+’ (RefWind) and ‘×’ (HiWind), respectively.

**Figure 6.**(

**a**) Correlation of wind effects from Figure 5 for heart rate (Δ

_{v}HR), rectal temperature (Δ

_{v}T

_{re}), mean skin temperature (Δ

_{v}T

_{sk}), and sweat rate (Δ

_{v}SR), respectively, with the wind effect on UTCI (Δ

_{v}UTCI), shown in Figure 3b, calculated for the temperature–humidity combinations of the experiments (cf. Figure 5). Spearman correlations (r

_{s}) and p−values are shown with smoothing splines and 95% confidence bands. Dashed vertical and horizontal lines indicate zero wind effects (Δ

_{v}= 0) for UTCI and the physiological responses, respectively, where negative values (Δ

_{v}< 0) indicate wind cooling and positive values (Δ

_{v}> 0) heating effects. (

**b**) UTCI performance in predicting heating wind effects (Δ

_{v}> 0) on HR, T

_{re}, T

_{sk}, and SR, respectively, expressed by sensitivity, specificity and accuracy.

**Figure 7.**Boxplots including the percentiles P0 (minimum), P25 (1st quartile), P50 (median), P75 (3rd quartile), and P100 (maximum) summarizing the effect of three levels of increased wind speed (v

_{a,10m}) on UTCI (Δ

_{v}UTCI) over air temperatures between 25 and 50 °C and vapor pressure of 0.1−5 kPa in relation to radiant heat load (ΔT

_{mrt}= T

_{mrt}− T

_{a}), cf. Figure A3.

**Table 1.**Fitted generalized additive models (GAMs) predicting experimental data on heart rate (HR), rectal temperature (T

_{re}), skin temperature (T

_{sk}), and sweat rate (SR), respectively, depending on combinations of air temperature (T

_{a}) and vapor pressure (p

_{a}), considering wind condition (RefWind, HiWind) as modifier and including a random subject effect. Abbreviations for model parameters, as in Equation (2).

HR (bpm) | T_{re} (°C) | T_{sk} (°C) | SR (g/h) | |
---|---|---|---|---|

Observations (#missing values) | 189 (9) | 198 (0) | 189 (9) | 186 (13) |

Goodness-of-fit | ||||

Adjusted R^{2} (%) | 78.8 | 76.2 | 88.6 | 89.9 |

Residual standard error | 7.6 | 0.2 | 0.4 | 120.1 |

Intercept µ | ||||

Mean estimate | 102.5 | 37.6 | 35.5 | 744.4 |

SE | 0.8 | 0.1 | 0.2 | 27.1 |

p-value | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

s(ID) | ||||

edf | 0.5 | 3.8 | 3.8 | 3.4 |

Ref.df | 4.0 | 4.0 | 4.0 | 4.0 |

F-value | 0.2 | 27.1 | 24.3 | 6.1 |

p-value | 0.2018 | <0.0001 | <0.0001 | <0.0001 |

te(T_{a}, p_{a}) | ||||

edf | 14.6 | 6.5 | 10.3 | 10.0 |

Ref.df | 19.0 | 8.2 | 14.0 | 13.4 |

F-value | 18.9 | 34.7 | 31.5 | 51.3 |

p-value | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

te_{Δv}(T_{a}, p_{a}) | ||||

edf | 4.0 | 4.0 | 5.5 | 4.5 |

Ref.df | 4.1 | 4.0 | 6.2 | 4.8 |

F-value | 10.8 | 7.0 | 4.8 | 8.3 |

p-value | <0.0001 | <0.0001 | 0.0001 | <0.0001 |

_{a}, p

_{a}): temperature–humidity effect (bivariate tensor product spline); te

_{Δv}(T

_{a}, p

_{a}): temperature–humidity-dependent wind effect of HiWind compared to RefWind (bivariate interaction spline).

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## Share and Cite

**MDPI and ACS Style**

Bröde, P.; Kampmann, B.
Temperature–Humidity-Dependent Wind Effects on Physiological Heat Strain of Moderately Exercising Individuals Reproduced by the Universal Thermal Climate Index (UTCI). *Biology* **2023**, *12*, 802.
https://doi.org/10.3390/biology12060802

**AMA Style**

Bröde P, Kampmann B.
Temperature–Humidity-Dependent Wind Effects on Physiological Heat Strain of Moderately Exercising Individuals Reproduced by the Universal Thermal Climate Index (UTCI). *Biology*. 2023; 12(6):802.
https://doi.org/10.3390/biology12060802

**Chicago/Turabian Style**

Bröde, Peter, and Bernhard Kampmann.
2023. "Temperature–Humidity-Dependent Wind Effects on Physiological Heat Strain of Moderately Exercising Individuals Reproduced by the Universal Thermal Climate Index (UTCI)" *Biology* 12, no. 6: 802.
https://doi.org/10.3390/biology12060802