## Abstract

This study measured sweat rates (m_{sw}) during high-altitude summer treks on Mt. Kilimanjaro to evaluate the efficacy of a recently developed fuzzy piecewise sweat prediction equation (*Ṗ*w,sol) for application to high-altitude conditions. We hypothesized that the *Ṗ*w,sol equation, adjusted for the barometric pressure (Pb) decreasing steadily at high altitude (*Ṗ*w,sol+Alt), would allow for a more accurate prediction of m_{sw} than *Ṗ*w,sol unadjusted for altitude (*Ṗ*w,sol_{SL}). Fifteen men (43 ± 16 yr; 80 ± 22 kg) and seven women (46 ± 16 yr; 77 ± 18 kg) wearing hiking clothes (clo ∼1.15; clothing evaporative potential = 0.27) and carrying light loads (9 ± 2 kg), were studied during morning and afternoon treks (∼2–3 h) while ascending from 2,829 m to 3,505 m. After each trek, m_{sw} was measured with specific biophysical parameters at 15-min intervals. During the trek day, Pb progressively declined (530 to 504 Torr), as solar radiation and ambient temperature (°C) rose transiently. During all treks, m_{sw} ranged from 68 to 393 g·m^{−2}·h^{−1} (0.14 to 0.79 l/h). For each subject, derived *Ṗ*w,sol_{SL} and *Ṗ*w,sol+Alt model outputs accurately predicted the morning and afternoon average m_{sw} within a root mean square error of 0.145 l/h. No differences were found between *Ṗ*w,sol_{SL} and *Ṗ*w,sol+Alt values. In conclusion, we report the first m_{sw} measured during outdoor high-altitude activities and determined that *Ṗ*w,sol_{SL} equation can be used to predict fluid needs during high-altitude activities without alterations for lower Pb. This model prediction provides a valid water planning tool for outdoor activities at high altitude up to 3,500 m.

- solar load
- hypobaric environments
- water requirements
- modeling prediction analyses

individuals sojourning at moderate-to-high altitudes may perform strenuous exercise and be exposed to environmental conditions, such as penetrating solar radiation (R_{sol}) and low ambient water vapor pressure (P_{w}), which can accentuate body water losses (10, 17). Altitude exposure is associated with marked body water deficits (15, 17) that may be sufficient to induce adverse functional outcomes (18, 30). Our laboratory recently demonstrated that moderate hypohydration (−4% body mass) at high altitude markedly impaired aerobic performance and increased symptoms associated with acute mountain sickness (3).

Water provides a logistical burden in mountainous terrains because it is usually carried on foot or air dropped (9) since roads are often absent at high altitude. Therefore, accurate water planning tools are needed that minimize the logistical burden of water transport while sustaining euhydration. Presently, no information exists for accurate water planning during moderate-to-high-altitude treks or military operations (9, 18). Of the potential avenues of water loss, such as increased respiratory water loss due to elevated minute ventilation, increased sweat rates (m_{sw}) provide the largest contribution during strenuous activity (18, 29). High-altitude environments might modify the sweating response as a result of reduced absolute humidity, which promotes skin evaporation due to a higher water vapor gradient (4, 21, 24). Knowledge regarding the impact of high altitude on m_{sw} is sparse, with limited data from laboratory conditions and no data from outdoor studies. Two of these laboratory studies have reported that sweat losses were lower (19, 36), and two others have reported that sweat losses were greater at high altitude (14, 35). Therefore, water planning based on sea level sweat loss predications may or may not accurately represent water needs at high altitude.

Our laboratory recently developed and validated a fuzzy piecewise equation that accurately predicts sweat losses (i.e., water needs) in cool, temperate, warm-hot, and transient solar load environments (*Ṗ*w,sol) (12, 13). The *Ṗ*w,sol equation is based on metabolic demands, clothing biophysical parameters, and environmental (heat and mass transfer) constraints (12, 13) and can be easily adjusted to the biophysical conditions of altitude exposure (19). The *Ṗ*w,sol equation (12) enables a substitution of the appropriate altitude barometric pressure (Pb) factors, integrating these factors into an adjusted algorithm (*Ṗ*w,sol+Alt) that impacts both the required evaporation (E_{req,Alt}) and maximum environmental evaporative capacity (E_{max,Alt}) and potentially allows predicted m_{sw} for such environments. However, it is unclear how a reduction in Pb at high altitudes will influence either actual or predicted m_{sw}.

This study measured m_{sw} during summer high-altitude treks on Mount Kilimanjaro with the purpose of evaluating the effectiveness of the *Ṗ*w,sol for high-altitude conditions. We hypothesized that adjusting the *Ṗ*w,sol equation using key biophysical coefficients altered by Pb at high altitude (*Ṗ*w,sol+Alt) would allow more accurate prediction of sweating rates at high altitude. This study provides the first m_{sw} information for high-altitude outdoor activities and potentially validates our sweat prediction equations (*Ṗ*w,sol and or *Ṗ*w,sol+Alt) for water planning at high altitudes.

## METHODS

#### Subjects.

Subjects were members of a commercial expedition to Mount Kilimanjaro. Seven women [mean ± SD; body weight (BW): 76.7 ± 17.6 kg; body surface area (BSA): 1.9 ± 0.3 m^{2}; age: 46 ± 16 yr] and 15 men (BW: 79.8 ± 21.8 kg; BSA: 2.0 ± 0.3 m^{2}; age: 43 ± 16 yr), who were healthy and reasonably fit, volunteered to take part in the investigation. Appropriate institutional review boards approved this study. Each volunteer attended a briefing outlining the purpose of the experiment and possible risks and completed a written, informed consent document before taking part in the investigation. Policies for protection of human subjects as prescribed in Army Regulations 70–25 and US Army Medical Research and Materiel Command Regulation 70–25 were adhered to by the investigators. The research was conducted in adherence with the provisions of 45 Code of Federal Regulations Part 46.

#### Experimental testing.

The expedition followed the established Lemosho Route toward the western slope of Mount Kilimanjaro in Tanzania, which consists of an ascent rate of ∼350 to 1,500 m each day. Experiments were conducted in summer (January) when warmer weather was expected. All data collection occurred while subjects trekked from Rain Forest Base Camp (2,829 m) to Shira Camp (3,505 m). Data collection was separated into two measurement periods: a morning trek (AM) from ∼0800 to ∼1200, followed by an afternoon trek (PM) from ∼1300 to ∼1630. During the treks, all subjects walked at a uniform pace that was recorded, and the terrain and elevation were noted. Urine specific gravity was measured from first morning urine before the AM trek.

Metabolic rates were calculated based on BW, external load (kg), walking speed (m/s), grade (%), and terrain using the equation of Pandolf et al. (25). This equation has been previously established to be reliable at altitude (8) with metabolic rates ≤730 W (384 W/m^{2}), which are greater than those in the present study. The respiratory exchange ratio was estimated at 0.9 for submaximal exercise and was assumed to be consistent during each trek (8).

#### Clothing.

The individuals were dressed with a lightweight hat, loose-fitting synthetic shirt, loose-fitted synthetic cargo-style pants, full gaiters, midweight hiking boots, light briefs, and a small day pack (mean load = 9.2 ± 2.3 kg). The total clothing ensemble insulation (I_{T}, clo) was estimated from similar US military clothing ensembles (evaluated on thermal manikins) as 1.0 to 1.15 clo (T. L. Endrusick, personal communication). Chang et al. (5) reported that, during walks in a hypobaric chamber up to 4,572 m [15,000 ft; atmospheric pressure (Patm) = 0.56 atm; Pb = 425 Torr], Pb did not significantly alter I_{T} values in the military clothing ensembles. The clothing ensemble in the Chang et al. study (5) was comparable with the present data set ensemble in this investigation. For both emulations of the prediction equations, the evaporative potential (i_{m}/clo) was estimated at 0.27 initially (11, 20, 21). Both the I_{T} and i_{m} and the effective air motion (*V*_{eff}) for heat exchange were subsequently adjusted for the effects of altitude (Pb) as quantified in Matthew et al. (21) and Kraning and Gonzalez (20) and as discussed in the following sections. Briefly, *V*_{eff} incorporates the vector quantity of air motion mass and direction around the subject, the air “pumping” coefficient (from limb movements), and walking speed.

#### m_{sw} measurements.

Total measured m_{sw} (g·m^{−2}·h^{−1}) and estimated sweat loss (m_{sw}; l/h) assume 1 g of lost mass is equivalent to 1 ml of lost sweat and was calculated and corrected as in previous studies (12, 13):
_{2}-O_{2} exchange; and DV is drink volume. At the beginning and end of the sweat loss measurement period (AM and PM treks), nude body mass was measured on a calibrated scale on a custom platform with built-in level. During the sweat loss measurement period, all ingested fluids, food, and urine volume and excrement were measured (Ohaus CL Series Compact Scales).

#### Physiological and biophysical measurements.

Skin temperature was measured using a skin temperature dermal patch sensor (Mini Mitter, Bend, OR) placed on the subject's chest (T_{sk},_{chest}) The chest provides the best single estimate of mean skin temperature (33) and is an important area for heat exchange (and sweating) during physical activity (31). This locus was also used to estimate evaporative and dry heat loss during the experimental runs.

Environmental conditions [ambient temperature (T_{a}), percent relative humidity, and wind velocity] were measured using an Onset Computer, Micro data logger (HOBO), model no. H21–002, with temperature, relative humidity sensor, global solar radiation (gSL; W/m^{2}) Silicon Pyranometer (S-LIB-M003), and Pb sensor. The respective gSL taken every 15 min per each subject's BSA (m^{2}) was then calculated using R_{sol} (12, 22).

In the heat flow form expressed by Matthew et al. (22),
_{sol} was subsequently transposed as W/m^{2} heat flux by dividing by each subject's BSA (R{sol′} = W/m^{2}). For analysis of the solar load in the heat balance, the value was adjusted for each subject by multiplying by the latent heat constant (0.68 W·h·g^{−1}) (10, 12, 24).

Mean radiant temperature (MRT, °C), was determined from (R′_{sol})⋅BSA and the T_{a} (°C) by (10, 20)
_{sol}. The heat balance equation (W/m^{2}) derived as a function of time (*t*) is:
*S* is the rate of body heat storage (and includes lumped effects of clothing latent heat storage) minus predicted metabolic heat production (M) minus external work rate (W_{k}) minus radiative (R) and convective heat loss (C), and E_{sk} = (E − E_{res} − C_{res} − E_{dif} − m_{res}). The variable (E) incorporates total sweat loss minus respiratory (E_{res}) and convective heat loss (C_{res}), minus skin diffusion (E_{dif}), less any metabolic heat loss (m_{res}). As implemented by previous biophysics analyses (5, 10, 24), C_{res} is affected by reduced Pb so that C_{res} = 0.0014·M·(34 − T_{a})·(Pb/760). Although hyperventilation occurs during reduced Pb, and E_{res} is increased with each subsequent increase in altitude, the equation E_{res} = 0.0023·M·(44 − P_{a}) is not known to be altered by Pb and, rather, changes only as ambient P_{w} (P_{a}, Torr) decreases or rises.

The evaporative (insensible) heat flux (E_{sk}) was determined by the sweat loss (m_{sw}) from *Eq. 1* using the Peters-Passmore analysis (7). In this analysis, all of the fluid losses include noneccrine sources, such as respiration, that would be augmented by hyperventilation due to decreasing Pb. Decreasing Pb also influences the maximal rate of evaporative heat loss from a fully wetted skin surface (E_{max}). E_{max} is a function of the vapor pressure gradient between the fully wetted skin surface and the air (P_{s,sk} − P_{w}), where P_{s,sk} is vapor pressure of saturated air at skin temperature, the evaporative heat transfer coefficient (h_{e}), and i_{m}, Woodcock's dimensionless factor for permeability of water vapor through clothing (10). The h_{e} is directly related to the convective heat transfer coefficient (h_{c}) by the Lewis Relationship (LR, 2.2°C/Torr or 16.5 K/kPa) (10). When evaporation is not restricted by clothing or by a humid environment, then E_{sk} = m_{sw}·λ, where m_{sw} is in g/h and λ is the heat of vaporization for sweat at 35°C (=0.68 W·h·g^{−1}).

The expression for E_{sk} above is generally for skin wettedness areas less than one or under conditions where evaporation of sweat is not restricted. During situations when the skin is fully wet with sweat, particularly during exercise with impermeable clothing (10) and there is excessive dripping (E_{drip}) or wasted sweat due to skin wettedness (*w*) > 1.0, E_{sk} for modeling (19, 20) purposes may be evaluated as:
*A*_{D} is the DuBois surface area (m^{2}), and P_{s,sk} is in Torr. Respiratory heat loss is also a part of the nonsweat loss avenue that is contained within in the Peters-Passmore evaluation in *Eq 1*. Here, (C_{res} + E_{res}) are directly related to ventilation rate and vary as a function of aerobic exercise intensity up to maximal levels. All of these factors are interrelated and influenced by decreases in Pb and variations in solar flux in the following manner:
_{m}/I_{T}) from skin diffusion through clothing layers increases, and the I_{T} (insulation and clothing resistance) is influenced by decreasing Pb, as shown in *Eq. 5a*.

We measured Pb every 15 min, but only used the end trek values in comparing predicted model output against actual m_{sw}. However, generally, in treks through various altitudes, the local Pb is often not known, but can be easily determined (19) by the following equation:

Similarly, the altitude/pressure-sensitive E_{max} can be computed for each altitude by (10, 22)
_{max,SL} is the sea level value (12). The I_{T and} i_{m} coefficients are also altered by *V*_{eff} (from walking and ambient wind speed) (10, 20, 24). Typically, the measured or computed Patm is inserted as a multiplier for *V*_{eff} (m/s) to compute altitude pressure-sensitive total clo [or total resistance, (R_{cl} + R_{a}), where R_{cl} is fabric clothing thermal resistance and R_{a} is ambient air thermal resistance along with fabric + skin-air gap resistances] in which
_{Tc} and I_{Tvc} include the clo and clo velocity transfer coefficients, respectively, for the subject's clothing ensemble.

The maximum evaporative power of the environment (E_{max,SL}) is categorically increased with decreasing Pb as altitude is increased, as described above. The sensible heat flux (R + C), or dry (W/m^{2}), can be estimated by heat flux from the chest (T_{sk,chest}) in the heat balance equation for this data set; this variable is influenced by changes in altitude, R_{sol}, and tissue skin conductance (skin blood flow) properties (10) as
_{o} in *Eq 9* is the operative temperature defined as the temperature in the isothermal environment impacted by R_{sol} during the treks as a function (*f*) of time; [h_{r} + h_{c}] is the combined heat transfer coefficient from radiative and convective heat transfer; the factor F_{cl} is the Burton thermal efficiency factor equivalent to, and estimated, by 1/[1+ 0.1545·(h_{r} + h_{c})·clo of the garment as a *f*(*V*_{eff}, Patm)] (10). All avenues of heat exchange and respective heat transfer coefficients were calculated as in previous studies (13).

#### Piecewise m_{sw} prediction equation.

The *Ṗ*w,sol equation (12) was modified by including changes in transient R_{sol} and altitude Pb (*Ṗ*w,sol+Alt), as well as transient R_{sol} with fixed sea level Pb (*Ṗ*w,sol_{SL}), which altered the equation coefficients. The E_{req,sol} (W/m^{2}) was derived by employing a time-based heat balance solution of (M − W_{k}) ± (R + C) + R_{sol} and transformed to g·m^{−2}·h^{−1} by dividing by the latent heat constant (λ = 0.68 W·h·g^{−1}). The E_{max} was derived from the respective *Ṗ*w_{x} [*x* = (solar + Alt) or (solar at sea level)] clothing and thermal coefficients. Core temperature was not measured but was assumed to fluctuate relative to metabolic rate and not vary by more than10% (19).

To derive (*Ṗ*w,sol+Alt) for this data set, E_{req,Alt} and E_{max,Alt} were each calculated following each trek period by analysis of the individual's heat balance using Pb (21) and T_{a}, P_{a} data. Calculations were done using observed Pb, R_{sol}, along with the respective h_{e} and h_{c}. The steady-state resultant sweat prediction equation is described as:
*Ṗ*w,sol_{SL}) model, only E_{req,sol} [M_{sk} ± (R + C) + R{sol′}] and E_{max,SL} [hypothetically assuming sea level coefficients (Pb = 1 atm; 760 mmHg)] were implemented for this data set. In this equation, M_{sk} equals the net heat flux from the interior body to the skin previously described (11), M_{sk} = (M − Wext − E_{res} − C_{res} − m_{res}), where W_{ext} represents external work based on activity (W/m^{2}) (24).

#### Statistics.

Data were analyzed using Statistica (version 10, Tulsa, OK) or Microsoft Excel statistical modules and solver. Simple Ordinary Least Squares (OLS) with Pearson-Product correlation coefficients (*r*) and appropriate *F*-tests (23, 27) and intraclass correlation coefficients (27) or multiple stepwise regressions were first used to analyze the dependence between variables. All but three subjects in the AM and PM treks were used in repeated manner, so the differences between means were also examined using paired *t*-tests to compare intraindividual measured and predicted sweat loss. The values were tested by ANOVA for paired and nonpaired samples, assuming two-sample equal variances. The assumptions of normality and homogeneity of variance for parametric procedures were checked using the Kolmogorov-Smirnov test. When the assumptions of normality or homogeneity of variance were not met, we used equivalent nonparametric tests (Kruskal-Wallis tests) for comparison of means of two independent samples (23). Following ANOVA, the data were tested using Tukey's post hoc for honestly significant differences for unpaired data (23). The differences pointed out in the results are statistically significant values *P* < 0.05.

The analyses of OLS are often pervaded by many limitations that cannot address reliability prediction of a given model's algorithm estimate tracking the actual data (27). Because of this fact, an additional analysis comparing residuals resulting from the deviation of model output minus actual vs. measured m_{sw} was carried out (27). The observed m_{sw} from the pooled data set from the two treks (*N* = 43 cases in 21 AM and 22 PM subjects) were compared with test against the theoretical predicted values of *Eqs. 10a* and *10b*, and resulting residuals (g·m^{−2}·h^{−1}) were analyzed (predicted model output minus actual) vs. observed m_{sw} (27) for each subset data. Additionally, each separate trek period (AM and PM) in which the predicted-actual (l/h) deviations from each model output were compared for each individual relative to an established zone of indifference (7). Finally, the sweat loss values (calculated in l/h) for each individual were compared for each of the two model prediction deviations to establish the average error derived by the root mean square error (RMSE) (16) defined for this data set as:
*F*_{i} is the forecasted values transposed to fluid output from the two models: *Ṗ*w,sol+Alt or *Ṗ*w,sol_{SL}; *O*_{i} is the observed value (l/h) for each subject; and *n* is number of observations.

## RESULTS

First morning urine specific gravity values were less than 1.012, suggesting that subjects were well hydrated (6). During the treks, fluid intake was encouraged, but hydration state was not assessed. There were no incidences of AMS during the AM or PM trek. During the trek from Rain Forest Camp to Shira Camp (from 2,829 m to 3,505 m), the subjects traversed open forest and moorlands and included a progressively declining Pb (Fig. 1*A*), periods of low/high solar load (R_{sol}, W/m^{2}) (Fig. 1*B*), and variable midday T_{a} (°C) (Fig. 1*C*), reaching a peak T_{a} of 26°C (with peak MRT ∼ 40°C). The AM and PM treks were completed when T_{a} were at their low ranges (Fig. 1*C*). The AM trek was 124 min, and the PM trek was 168 min in duration. Table 1 compares the environmental and thermal values at completion of the AM and PM treks. R_{sol}, MRT were higher (*P* < 0.01) for the AM compared with PM, but chest (R+C) was lower in the AM trek (Table 1).

The measured m_{sw} from the individuals ranged from 0.13 to 0.79 l/h (65 to 393 g·m^{−2}·h^{−1}) and 0.27 to 0.54 l/h (136 to 270 g·m^{−2}·h^{−1}) in the AM and PM treks, respectively. Table 2 provides the mean measured and the mean predicted (*Ṗ*w,sol_{SL} and *Ṗ*w,sol+Alt) m_{sw} outputs estimated for the AM and PM treks. Mean m_{sw} were not different between measured (0.41 ± 0.16 l/h AM and 0.38 ± 0.17 l/h PM) and predicted values. Measured values and both predicted model outputs were higher (*P* < 0.01) during the AM than PM trek. The higher m_{sw} during the AM trek likely reflected the antecedent higher solar load (MRT and effective radiant flux), which should increase thermoregulatory sweating (10, 12).

The initial goodness-of-fit criterion used to depict discrepancy between the prediction equations and the measured m_{sw} was first tested by OLS and use of Pearson's *r* values. AM data (*N* = 21 subjects) were regressed separately from the PM data (*N* = 22), as one subject did not participate in the AM trek and another in the PM trek. The specific OLS analysis of the AM treks resulted in the following equations (g·m^{−2}·h^{−1}):
_{sw} for the AM trek was not a significant linear predictor (*r* = 0.27) of measured m_{sw} for this data set. Four subjects with high m_{sw} > 250 g·m^{−2}·h^{−1} drove the slope away from the identity line (prediction = observed), resulting in the low correlation. For the PM trek data (*N* = 22), OLS equations were:

Figure 2 is a residual plot of regression analysis for purposes of checking the uniformity of error which compares each model predicted msw over the two treks. There was a strong correlation (*r*^{2} = −0.67) (*F*-ratio = 81,1, *P* < 0.001) (1) between these variables, and that shows both model outputs are statistically robust predictors of sweating rate and within a zone of indifference (±0.125 l/h or 65 g·m^{−2}·h^{−1}) established in our earlier work (7).

Figure 3 displays a comparison of each individual subject's predicted minus the measured m_{sw}, relative to the previously mentioned zone of indifference [shaded bar; ±0.125 l/h; m_{sw} transposed into fluid outputs (l/h)] (7). For the AM trek (Fig. 3*A*), there was close agreement for both model's predicted values, and three subjects fell above and three subjects fell below the zone of indifference. Similarly, for the PM trek (Fig. 3*B*), there was close agreement for both model's predicted values, and two subjects fell above and three below the zone of indifference.

The RMSE was calculated to evaluate each model's deviation (methods, *Eq. 11*) from measured m_{sw}. It can be noted that, with the exception of *subject 20*, different subjects fell outside the zone of indifference for the AM and PM treks. The RMSE for both prediction equations during the AM and PM treks was 0.145 l/h (∼75 g·m^{−2}·h^{−1}), which approximates the previously established zone of indifference (7).

## DISCUSSION

This study is the first investigation to accurately measure m_{sw} during outdoor, high-altitude treks and to provide a validated prediction model for activities up to 3 METS. Twenty-two subjects completed two treks at ∼3,200 m while ascending Mt. Kilimanjaro and with changing heat stress conditions while their m_{sw} were carefully measured at high altitude. We found that *1*) measured sweating rates ranged from 0.14 to 0.79 l/h (68 to 393 g·m^{−2}·h^{−1}) during high-altitude treks; and *2*) the “altitude adjusted” (*Ṗ*w,sol+Alt) equation was equally accurate to the sea level *Ṗ*w,sol_{SL} model output (RMSE of 0.145 l/h) in predicting sweating rates. We originally hypothesized that adjusting the *Ṗ*w,sol equation using key biophysical coefficients altered by Pb at high altitude (*Ṗ*w,sol+Alt) would result in a more accurate prediction of sweating rates at high altitude. As both models showed equivalent prediction outputs compared with actual values within a zone of indifference (7) of ±0.125 l/h reported in other studies (12, 13), our hypothesis was incorrect. Despite alterations in E_{req,Alt} and E_{max,Alt} as a result of lower Pb, the established *Ṗ*w,sol_{SL} equation can be used to predict fluid needs during high-altitude activities up to 3,500 m, without alterations for lower Pb. The provided information has importance in planning water needs for high-altitude treks and/or various operations.

Measured m_{sw} ranged from 0.14 to 0.79 l/h (68 to 393 g·m^{−2}·h^{−1}) during high-altitude treks as the environmental conditions changed (Fig. 1), especially with fluctuating solar load during the two treks. The measured sweating rates are similar to those reported for wide military activities in temperate-warm climates (18) at sea level and unremarkable compared with those for athletes training and competing in hot weather (28). The metabolic rates for our subjects (166 W/m^{2}; ∼3 METS) are considered moderate-intensity work for military activities (26), but are lower than those often reported during athletic competition and training (28). It is difficult to relate the m_{sw} measured in the field in the present study to those in the literature, as few studies have measured m_{sw} at high altitude, and none has done so outside of laboratory conditions.

Studies observing sweating rates in high-altitude conditions have reported higher (14, 35), lower (19, 36), or unchanged (2) sweating rates compared with sea level. Greenleaf et al. (14) reported a small increase in sweating rate (222 to 257 g·m^{−2}·h^{−1}; *P* < 0.05) from 350 m to a simulated altitude of 4,000 m. Varene and colleagues (35) measured sweating rate at sea level (50 m, Paris) and at high altitude (3,800 m, La Paz) in a laboratory and reported sweating rates of 141 ± 12 and 190 ± 22 g·m^{−2}·h^{−1} at 50 m and 3,800 m, respectively. In contrast, using doubly labeled water, Westerterp et al. (36) estimated water turnover before and after arrival at a 4,350-m laboratory and reported evaporative water loss decreased from 2.5 to 1.3 l/day. Kolka and colleagues (19) performed a comprehensive study on control of local sweat responses during exercise at sea level and simulated altitudes of 2,596 m and 4,575 m. They only measured local m_{sw} that cannot be accurately converted to whole body values (33) and found that local m_{sw} were lower at moderate and high altitude. However, since the exercise work rates were altitude-specific relative intensities, the metabolic rates were also lower at moderate and high altitude than at sea level. Buskirk (2) measured total body water turnover via doubly-labeled water in track athletes at sea level and 4,000 m over ∼7 wk and reported no differences when initially arriving at altitude, at *days 8* and *44* of altitude exposure, and at *day 70* when returning to sea level. Given the equivocal findings in the literature and the theoretical postulation that lower Pb could alter E_{req} and E_{max}, it was reasonable to assume that high-altitude conditions could alter sweating rate. Due to the lack of a control condition, we were not able, nor did we endeavor, to assess whether m_{sw} changes as a function of altitude. While we did not study the impact of altitude on m_{sw} responses, given our findings the differences between sea level and altitude (3,500 M) may be equivocal.

Outdoor high-altitude conditions pose a complex thermal environment due to an elevated vapor transfer gradient and high radiant loads, conditions that could significantly impact the ability to predict water needs from known equations (e.g., *Ṗ*w,sol). This study provided an opportunity to further validate our m_{sw} prediction equation (12), developed and validated for sea level environments (>500 data cases), with additional empirical data collected over a broader range of environmental conditions involving high-altitude exercise using appropriate biophysical modifications. During the treks, transient solar load, Pb, and T_{a} varied (Fig. 1), providing an ideal set of conditions. Adjustment of P_{w} coefficient inputs estimated for the appropriate altitude factors (E_{req,Alt} and E_{max,Alt}) compared with the existing sea level *Ṗ*w,sol equation provided a nominally higher prediction sweat loss value (Figs. 2 and 3), but no significant differences (Table 2). Despite the inherent assumptions in some of the variables used to predict m_{sw} [previously described (12)], the heterogeneity of our subject population (18–66 yr), and measured m_{sw} (from 0.14 to 0.79 l/h), the root mean square was low, and the predicted and measured sweating rate values were similar and were less than the a priori zone of indifference (<0.125 l/h) (7). Therefore, adjustments to the P_{w} coefficient inputs for altitude factors (E_{req,Alt} and E_{max,Alt}) up to ∼3,500 m did not result in a more accurate prediction of m_{sw}. However, it is unclear if lower Pb at altitudes greater than 3,500 m would sufficiently alter E_{req} and E_{max} such that the *Ṗ*w,sol_{SL} equation would need to be adjusted.

Interestingly, the measured and predicted m_{sw} were slightly higher during the AM trek when MRT was elevated. This likely demonstrated the sensitivity of our m_{sw} measurements (approximately +30 ml in AM vs. PM) and our prediction equations (approximately +25 ml in AM vs. PM) to differentiate between AM and PM treks for the slightly elevated MRT (+4.5°C in AM). It is well established that thermoregulatory sweating is dependent on numerous factors (32, 34). Despite the fact that ambient air temperatures tend to be lower at altitude (increasing dry heat exchange), at any given T_{a}, elevated R_{sol} and resultant MRT should be expected to increase m_{sw} (12). Likewise, it should be noted that, due to alternating cloud cover, R_{sol} fluctuated during each trek and was not at consistent daily peak level (see Fig. 1). Higher m_{sw} would have been expected during treks conducted at a peak MRT; however, that impact would not be as great as working at a substantially higher metabolic rate during the trek (8).

In conclusion, *1*) we report the first m_{sw} measured during outdoor, high-altitude activities; and *2*) we determined that sea level-adjusted *Ṗ*w,sol_{SL} and *Ṗ*w,sol+Alt prediction equations were equally valid in predicting m_{sw}. Given this finding, the established *Ṗ*w,sol_{SL} equation can be used to predict fluid needs during high-altitude activities without alterations for lower Pb. In addition, these data demonstrate the robustness of the *Ṗ*w,sol to predict m_{sw} under a wide variety of environmental conditions (12, 13) at high altitudes of up to ∼3,500 m. The provided information has importance in planning water needs for high-altitude treks/operations, as water provides a logistical burden and dehydration impairs performance during high altitude operations.

## GRANTS

This study was a flag expedition of The Explorers Club, New York City, NY, and funding was provided by the US Army Medical Research and Material Command.

## DISCLAIMER

The opinions or assertions contained herein are the private views of the authors and should not be construed as official or reflecting the views of the Army or the Department of Defense and/or the New Mexico State University Regents.

## DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

## AUTHOR CONTRIBUTIONS

Author contributions: R.R.G., R.W.K., S.R.M., S.W.H., and M.N.S. conception and design of research; R.R.G., R.W.K., S.R.M., and S.W.H. performed experiments; R.R.G. and R.W.K. analyzed data; R.R.G., R.W.K., and M.N.S. interpreted results of experiments; R.R.G. and R.W.K. prepared figures; R.R.G., R.W.K., S.R.M., and M.N.S. drafted manuscript; R.R.G., R.W.K., S.R.M., S.W.H., and M.N.S. edited and revised manuscript; R.R.G., R.W.K., S.R.M., and M.N.S. approved final version of manuscript.

## ACKNOWLEDGMENTS

We appreciate the efforts of the volunteer subjects and thank them for participation in the various experimental protocols. We also thank Drs. Samuel N. Cheuvront and Nisha Charkoudian for editorial assistance.