Case study of skin temperature and thermal perception in a hot outdoor environment

Focusing on the understanding and the estimation of the biometeorological conditions during summer in outdoor places, a field study was conducted in July 2010 in Athens, Greece over 6 days at three different sites: Syntagma Square, Ermou Street and Flisvos coast. Thermo-physiological measurements of five subjects were carried out from morning to evening for each site, simultaneously with meteorological measurements and subjective assessments of thermal sensation reported by questionnaires. The thermo-physiological variables measured were skin temperature, heat flux and metabolic heat production, while meteorological measurements included air temperature, relative humidity, wind speed, globe temperature, ground surface temperature and global radiation. The possible relation of skin temperature with the meteorological parameters was examined. Theoretical values of mean skin temperature and mean radiant temperature were estimated applying the MENEX model and were compared with the measured values. Two biometeorological indices, thermal sensation (TS) and heat load (HL)—were calculated in order to compare the predicted thermal sensation with the actual thermal vote. The theoretically estimated values of skin temperature were underestimated in relation to the measured values, while the theoretical model of mean radiant temperature was more sensitive to variations of solar radiation compared to the experimental values. TS index underestimated the thermal sensation of the five subjects when their thermal vote was ‘hot’ or ‘very hot’ and overestimated thermal sensation in the case of ‘neutral’. The HL index predicted with greater accuracy thermal sensation tending to overestimate the thermal sensation of the subjects.     

Modelling radiation fluxes in simple and complex environments—application of the RayMan model

The most important meteorological parameter affecting the human energy balance during sunny weather conditions is the mean radiant temperature T_mrt. It considers the uniform temperature of a surrounding surface giving off blackbody radiation, which results in the same energy gain of a human body given the prevailing radiation fluxes. This energy gain usually varies considerably in open space conditions. In this paper, the model ‘RayMan’, used for the calculation of short- and long-wave radiation fluxes on the human body, is presented. The model, which takes complex urban structures into account, is suitable for several applications in urban areas such as urban planning and street design. The final output of the model is, however, the calculated T_mrt, which is required in the human energy balance model, and thus also for the assessment of the urban bioclimate, with the use of thermal indices such as predicted mean vote (PMV), physiologically equivalent temperature (PET) and standard effective temperature (SET*). The model has been developed based on the German VDI-Guidelines 3789, Part II (environmental meteorology, interactions between atmosphere and surfaces; calculation of short- and long-wave radiation) and VDI-3787 (environmental meteorology, methods for the human-biometeorological evaluation of climate and air quality for urban and regional planning. Part I: climate). The validation of the results of the RayMan model agrees with similar results obtained from experimental studies.     

A study of human skin and surface temperatures in stable and unstable thermal environments

Skin temperature is a common physiological parameter that reflects human thermal responses. The purpose of this research was to investigate the effects of radiant temperature on human skin temperature and surface temperature in stable and unstable thermal environments. For a clothed human body, the skin temperature is the surface temperature of the skin, while the surface temperature is the outer surface temperature of the clothes. For this aim, the radiant temperature from 26 to 38 °C and then from 38 to 26 °C was controlled in three different ways; in stable condition keeping stable above 40 min, in unstable condition at a rate of 2 °C/5 min, and in another unstable condition at a rate of 2 °C/10 min. Experimental data showed that at the same radiant temperature, the local skin/surface temperatures during the radiant temperature decrease were higher compared to those during the radiant temperature increase. During the radiant temperature increase/decrease, the increments/decrements of the mean skin temperature and the mean surface temperature decreased gradually from the stable condition, 2 °C/10 min to 2 °C/5 min. Compared to surface temperature, the faster the radiant temperature changed, the more obviously the change in skin temperature was delayed. These data demonstrated that the human body has physiological adaptability to unstable thermal environments.     

Evaluation of mean skin temperature formulas by infrared thermography

 To study the reliabiliity of formulas for calculating mean skin temperature (T _sk), values were computed by 18 different techniques and were compared with the mean of 10,841 skin temperatures measured by infrared thermography. One hundred whole-body infrared thermograms were scanned in ten resting males while changing the air temperature from 40° C to 4° C. Local, regional average and mean skin temperatures were obtained using an image processing system. The agreement frequency, defined as the percentage of the calculated T _sk values which agreed with the corresponding infrared thermographic T _sk within ±0.2° C, ranged for with the various formulas from 7% to 80%. In many sites, the local skin temperature did not coincide with the regional average skin temperature. When the local skin temperatures which showed the highest percentage similarity to the regional average skin temperature within ±0.4° C were applied to the formula, the agreement frequency was markedly improved for all formulas. However, the agreement frequency was not affected by changing the weighting factors from specific constants to individually measured values of regional surface area. By applying the physiologically reliable accuracy range of ±0.2° C in the moderate and ±0.4° C in the cool condition, agreement frequencies of at least 95% were observed in formulas involving seven or more skin temperature measurement sites, including the hand and foot. We conclude that calculation of a reliable mean skin temperature must involve more than seven skin temperature measurement sites regardless of ambient temperature. Optimal sites for skin temperature measurement are proposed for various formulas. Received: 2 December 1996 / Accepted: 25 June 1997     

The energy budget of man: Variations with aspect in a downtown urban environment

The energy budget of man is computed and used to assess the microclimatic variation that can occur in a downtown urban environment through the effects of direction of exposure and open sky view factor. On sunny days the exposure to direct beam solar radiation was the most important factor in creating climatic differences. This directly contributed energy to man and warmed the radiant and air temperature environments. On a cloudy day very little variation in the radiation, temperature and humidity regimes occurred. Wind became the dominant factor with man experiencing a greater heat loss at windward locations. With the assumptions used in this study convective heat flux was responsible for the greatest heat losses in man.     

Prediction of mean skin temperature in warm environments

The data collected by the authors in four experimental series have been analysed together with data from the literature, to study the relationship between mean skin temperature and climatic parameters, subject metabolic rate and clothing insulation. The subjects involved in the various studies were young male subjects, unacclimatized to heat. The range of conditions examined involved mean skin temperatures between 33 degrees C and 38 degrees C, air temperatures (Ta) between 23 degrees C and 50 degrees C, ambient water vapour pressures (Pa) between 1 and 4.8 kPa, air velocities (Va) between 0.2 and 0.9 m.s-1, metabolic rates (M) between 50 and 270 W.m-2, and Clo values between 0.1 and 0.6. In 95% of the data, mean radiant temperature was within +/- 3 degrees C of air temperature. Based on 190 data averaged over individual values, the following equation was derived by a multiple linear regression technique: Tsk = 30.0 + 0.138 Ta + 0.254 Pa-0.57 Va + 1.28.10(-3) M-0.553 Clo. This equation was used to predict mean skin temperature from 629 individual data. The difference between observed and predicted values was within +/- 0.6 degrees C in 70% of the cases and within +/- 1 degrees C in 90% of the cases. It is concluded that the proposed formula may be used to predict mean skin temperature with satisfactory accuracy in nude to lightly clad subjects exposed to warm ambient conditions with no significant radiant heat load.     

SOLWEIG 1.0 – Modelling spatial variations of 3D radiant fluxes and mean radiant temperature in complex urban settings

The mean radiant temperature, T_mrt, which sums up all shortwave and longwave radiation fluxes (both direct and reflected) to which the human body is exposed is one of the key meteorological parameters governing human energy balance and the thermal comfort of man. In this paper, a new radiation model (SOLWEIG 1.0), which simulates spatial variations of 3D radiation fluxes and T_mrt in complex urban settings, is presented. The T_mrt is derived by modelling shortwave and longwave radiation fluxes in six directions (upward, downward and from the four cardinal points) and angular factors. The model requires a limited number of inputs, such as direct, diffuse and global shortwave radiation, air temperature, relative humidity, urban geometry and geographical information (latitude, longitude and elevation). The model was evaluated using 7 days of integral radiation measurements at two sites with different building geometries – a large square and a small courtyard in Göteborg, Sweden (57°N) – across different seasons and in various weather conditions. The evaluation reveals good agreement between modelled and measured values of T_mrt, with an overall good correspondence of R ²?=?0.94, (p?相似文献   

Time-of-day effects of exposure to solar radiation on thermoregulation during outdoor exercise in the heat

High solar radiation has been recognised as a contributing factor to exertional heat-related illness in individuals exercising outdoors in the heat. Although solar radiation intensity has been known to have similar time-of-day variation as body temperature, the relationship between fluctuations in solar radiation associated with diurnal change in the angle of sunlight and thermoregulatory responses in individuals exercising outdoors in a hot environment remains largely unknown. The present study therefore investigated the time-of-day effects of variations in solar radiation associated with changing solar elevation angle on thermoregulatory responses during moderate-intensity outdoor exercise in the heat of summer. Eight healthy, high school baseball players, heat-acclimatised male volunteers completed a 3-h outdoor baseball trainings under the clear sky in the heat. The trainings were commenced at 0900 h in AM trial and at 1600 h in PM trial each on a separate day. Solar radiation and solar elevation angle during exercise continued to increase in AM (672–1107 W/m² and 44–69°) and decrease in PM (717–0 W/m² and 34–0°) and were higher on AM than on PM (both P < 0.001). Although ambient temperature (AM 32–36°C, PM 36–30°C) and wet-bulb globe temperature (AM 31–33°C, PM 34–27°C) also continued to increase in AM and decrease in PM, there were no differences between trials in these (both P > 0.05). Tympanic temperature measured by an infrared tympanic thermometer and mean skin temperature were higher in AM than PM at 120 and 180 min (P < 0.05). Skin temperature was higher in AM than PM at the upper arm and thigh at 120 min (P < 0.05) and at the calf at 120 and 180 min (both P < 0.05). Body heat gain from the sun was greater during exercise in AM than PM (P < 0.0001), at 0–60 min in PM than AM (P < 0.0001) and at 120–180 min in AM than PM (P < 0.0001). Dry heat loss during exercise was greater at 0–60 min (P < 0.0001), and lower at 60–120 min (P < 0.05) and 120–180 min (P < 0.0001) in AM than PM. Evaporative heat loss during exercise was greater in PM than AM at 120–180 min (P < 0.0001). Total (dry + evaporation) heat loss at the skin was greater during exercise in PM than AM (P < 0.0001), at 0–60 min in AM than PM (P < 0.0001) and at 60–120 and 120–180 min in PM than AM (P < 0.05 and 0.0001). Heart rate at 120–150 min was also higher in AM than PM (P < 0.05). Neither perceived thermal sensation nor rating of perceived exertion was different between trials (both P > 0.05). The current study demonstrates a greater thermoregulatory strain in the morning than in the afternoon resulting from a higher body temperature and heart rate in relation to an increase in environmental heat stress with rising solar radiation and solar elevation angle during moderate-intensity outdoor exercise in the heat. This response is associated with a lesser net heat loss at the skin and a greater body heat gain from the sun in the morning compared with the afternoon.     

Comparison of different methods of estimating the mean radiant temperature in outdoor thermal comfort studies

Correlations between outdoor thermal indices and the calculated or measured mean radiant temperature T_mrt are in general of high importance because of the combined effect on human energy balance in outdoor spaces. The most accurate way to determine T_mrt is by means of integral radiation measurements, i.e. measuring the short- and long-wave radiation from six directions using pyranometers and pyrgeometers, an expensive and not always an easily available procedure. Some studies use globe thermometers combined with air temperature and wind speed sensors. An alternative way to determine T_mrt is based on output from the RayMan model from measured data of incoming global radiation and morphological features of the monitoring site in particular sky view factor (SVF) data. The purpose of this paper is to compare different methods to assess the mean radiant temperature T_mrt in terms of differences to a reference condition (T_mrt calculated from field measurements) and to resulting outdoor comfort levels expressed as PET and UTCI values. The T_mrt obtained from field measurements is a combination of air temperature, wind speed and globe temperature data according to the forced ventilation formula of ISO 7726 for data collected in Glasgow, UK. Four different methods were used in the RayMan model for T_mrt calculations: input data consisting exclusively of data measured at urban sites; urban data excluding solar radiation, estimated SVF data and solar radiation data measured at a rural site; urban data excluding solar radiation with SVF data for each site; urban data excluding solar radiation and including solar radiation at the rural site taking no account of SVF information. Results show that all methods overestimate T_mrt when compared to ISO calculations. Correlations were found to be significant for the first method and lower for the other three. Results in terms of comfort (PET, UTCI) suggest that reasonable estimates could be made based on global radiation data measured at the urban site or as a surrogate of missing SR data or globe temperature data recorded at the urban area on global radiation data measured at a rural location.     

The effect of Sub-MAC anesthesia and the radiation setting on repeated tail flick testing in rats.

The tail flick (TF) response is regarded as a spinal reflex that is influenced by supraspinal structures. The TF test using radiant heat is the most common way to assess pain perception; however, there are few reports dealing with the heat source's properties and score consistency. This study examined the usefulness of light anesthesia for suppressing supraspinal signals and the effects of radiant heat on skin temperature during TF testing. The fluctuations of TF latency over one hour were evaluated while the rats were given oxygen and 0%, 0.5%, 1.0%, or 1.5% isoflurane. The stimulator's infrared radiant (IR) power flux was measured over time, and the tail skin surface temperature was predicted using a non-linear regression equation. TF latencies were measured at various heat source intensities, and response temperatures were estimated. Inhalation anesthesia suppressed the TF reflex according to the inspiratory concentration of the volatile anesthetic. IR power fluxes reached constant power 2.5 s after the stimulator was turned on, and the predicted skin temperature depended on the maximum IR power flux of the IR intensity and the radiation time. One percent isoflurane inhalation and an IR20 heat intensity (which was 161.5 mW/cm(2) and resulted in a skin temperature of 65 degrees C after 10 s of radiation) provided reliable TF latencies on repeated TF testing. Given these results, it can be concluded that the stimulator setting influenced TF latency, and that the inhalation of light anesthesia provided consistent scores on repeated TF testing.     

Melanism and diel activity of alpine Colias (Lepidoptera: Pieridae)

Summary The hypothesis that increased melanism provides a benefit in prolonging diel activity through more efficient absorption of solar radiation was tested in the field on a population of alpine Colias sulphur butterflies. A marked increase in the duration of flight and feeding behaviour existed for melanistic individuals when compared to lighter individuals under cool temperatures and low intensity solar radiation. More melanistic butterflies moved longer distance per day, and emigrated from the population at a faster rate. At high temperature and high radiant load lighter coloured individuals appeared more active. This is the first field demonstration of the advantage of melanism for increasing activity of ectotherms in cold environments.     

Thermal equilibrium of goats

The effects of air temperature and relative humidity on thermal equilibrium of goats in a tropical region was evaluated. Nine non-pregnant Anglo Nubian nanny goats were used in the study. An indirect calorimeter was designed and developed to measure oxygen consumption, carbon dioxide production, methane production and water vapour pressure of the air exhaled from goats. Physiological parameters: rectal temperature, skin temperature, hair-coat temperature, expired air temperature and respiratory rate and volume as well as environmental parameters: air temperature, relative humidity and mean radiant temperature were measured. The results show that respiratory and volume rates and latent heat loss did not change significantly for air temperature between 22 and 26 °C. In this temperature range, metabolic heat was lost mainly by convection and long-wave radiation. For temperature greater than 30 °C, the goats maintained thermal equilibrium mainly by evaporative heat loss. At the higher air temperature, the respiratory and ventilation rates as well as body temperatures were significantly elevated. It can be concluded that for Anglo Nubian goats, the upper limit of air temperature for comfort is around 26 °C when the goats are protected from direct solar radiation.     

Orientation to solar radiation in black wildebeest (<Emphasis Type="Italic">Connochaetes gnou</Emphasis>)

We recorded the body axis orientation of free-living black wildebeest relative to incident solar radiation and wind. Observations were made on three consecutive days, on six occasions over the course of 1 year, in a treeless, predominantly cloudless habitat. Frequency of orientation parallel to incident solar radiation increased, and perpendicular to incident solar radiation decreased, as ambient dry-bulb temperature or solar radiation intensity increased, or wind speed decreased. We believe these changes were mediated via their effect on skin temperature. Parallel orientation behavior was more prominent when the wildebeest were standing without feeding than it was when they were feeding. We calculate that a black wildebeest adopting parallel orientation throughout the diurnal period would absorb 30% less radiant heat than the same animal adopting perpendicular orientation. Parallel orientation was reduced at times when water was freely available, possibly reflecting a shift from behavioral to autonomic thermoregulatory mechanisms. The use of orientation behavior by black wildebeest is well developed and forms part of the suite of adaptations that help them to maintain heat balance while living in a shadeless, often hot, environment.     

Modelling radiation fluxes in simple and complex environments: basics of the RayMan model

Short- and long-wave radiation flux densities absorbed by people have a significant influence on their energy balance. The heat effect of the absorbed radiation flux densities is parameterised by the mean radiant temperature. This paper presents the physical basis of the RayMan model, which simulates the short- and long-wave radiation flux densities from the three-dimensional surroundings in simple and complex environments. RayMan has the character of a freely available radiation and human-bioclimate model. The aim of the RayMan model is to calculate radiation flux densities, sunshine duration, shadow spaces and thermo-physiologically relevant assessment indices using only a limited number of meteorological and other input data. A comparison between measured and simulated values for global radiation and mean radiant temperature shows that the simulated data closely resemble measured data.     

Thermal radiation absorbed by dairy cows in pasture

The goal of the present paper was to assess a method for estimating the thermal radiation absorbed by dairy cows (0.875 Holstein–0.125 Guzerath) on pasture. A field test was conducted with 472 crossbred dairy cows in three locations of a tropical region. The following environmental data were collected: air temperature, partial vapour pressure, wind speed, black globe temperature, ground surface temperature and solar radiation. Average total radiation absorbed by animals was calculated as R_abs = 640.0 ±3.1 W.m ^{- 2} {R_{abs}} = 640.0 \pm 3.1\, W.{m^{ - 2}} . Absorbed short-wave radiation (solar direct, diffuse and reflected) averaged 297.9 ± 2.7 W m⁻²; long wave (from the sky and from terrestrial surfaces) averaged 342.1 ± 1.5 W m⁻². It was suggested that a new environmental measurement, the effective radiant heat load (ERHL), could be used to assess the effective mean radiant temperature ( T_\textmr^* ) \left( {T_{\text{mr}}^* } \right) . Average T_\textmr^* T_{\text{mr}}^* was 101.4 ± 1.2°C, in contrast to the usual mean radiant temperature, T_mr = 65.1 ±0.5^° C {T_{mr}} = 65.1 \pm 0.5^\circ C . Estimates of T_\textmr^* T_{\text{mr}}^* were considered as more reliable than those of T _mr in evaluating the thermal environment in the open field, because T _mr is almost totally associated only with long wave radiation.     

Wing pigmentation in Calopteryx damselflies: a role in thermoregulation?

Body melanization may show adaptive variation related to thermoregulation ability, and it is to be expected that the degree of melanization will change among populations or closely related species across environmental gradients of solar radiation and/or environmental temperature. Some melanized secondary sexual traits may also play a role in sexual selection, leading to interpopulation variation, which would not be predicted by thermoregulation pressures alone. We studied the relationships between the interpopulation variation in wing pigmentation level (i.e. melanized secondary sexual trait) of two closely related species of Calopteryx damselfly, and both solar radiation and maximum environmental temperature estimates. Wing pigmentation differs between these species, is gender specific and is used in species' discrimination. Only Calopteryx virgo meridionalis males showed a significant negative partial correlation between wing pigmentation degree and temperature. However, C. virgo meridionalis females showed a positive significant partial correlation between wing pigmentation degree and solar radiation. Wing pigmentation in Calopteryx xanthostoma males was not related to solar radiation or temperature. Thus, thermoregulation pressures poorly explained the observed variations in wing pigmentation between populations, although they might have an adaptive significance at the species' level. As wing pigmentation showed important latitudinal variation, several other selection pressures which might act on melanized traits are briefly discussed. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 103 , 36–44.     

Distinct patterns of changes in surface energy budget associated with forestation in the semiarid region

Land use and land cover changes greatly influence surface energy balance and consequently climate, and are likely to be associated with the persistent predictions of warming and drying throughout the Mediterranean and other regions. We specifically address the question of how the high radiation load and suppressed latent heat flux, intrinsic to dry regions, interact with land use changes and climate in these environments. We use for this purpose a detailed 6‐year (2003–2008) study of the redistribution of the radiation load in an open‐canopy pine forest. The results show that compared with the background shrubland, there was a 23.8 W m^?2 increase in shortwave radiation load on the forest (to a mean annual net solar radiation of 211 W m^?2) associated with a decrease in albedo of 0.1. Surface (skin) temperature in the forest was lower than in the shrubland (by ～5 °C on average) due to an efficient ‘convector effect’ and the production of a large sensible heat flux (up to 926 W m^?2 in summer), which effectively shifted heat from the canopy to the overlying boundary layer. The cooler forest skin temperature resulted in suppression of upwelling longwave radiation (by 25 W m^?2, annual average), further increasing the forest radiation load (mean annual net radiation of 116 and 67 W m^?2 for forest and shrubland, respectively). This suppression also resulted in a local ‘canopy greenhouse effect’, where upwelling longwave radiation from the ground to the canopy was larger than from the canopy to the atmosphere (by up to 150 W m^?2 in summer) and was associated with ～3 °C warming below the canopy. The ability of the dry productive forest to deal with the high radiation load indicates the potential for afforestation in dry areas.     

Deriving the operational procedure for the Universal Thermal Climate Index (UTCI)

The Universal Thermal Climate Index (UTCI) aimed for a one-dimensional quantity adequately reflecting the human physiological reaction to the multi-dimensionally defined actual outdoor thermal environment. The human reaction was simulated by the UTCI-Fiala multi-node model of human thermoregulation, which was integrated with an adaptive clothing model. Following the concept of an equivalent temperature, UTCI for a given combination of wind speed, radiation, humidity and air temperature was defined as the air temperature of the reference environment, which according to the model produces an equivalent dynamic physiological response. Operationalising this concept involved (1) the definition of a reference environment with 50% relative humidity (but vapour pressure capped at 20 hPa), with calm air and radiant temperature equalling air temperature and (2) the development of a one-dimensional representation of the multivariate model output at different exposure times. The latter was achieved by principal component analyses showing that the linear combination of 7 parameters of thermophysiological strain (core, mean and facial skin temperatures, sweat production, skin wettedness, skin blood flow, shivering) after 30 and 120 min exposure time accounted for two-thirds of the total variation in the multi-dimensional dynamic physiological response. The operational procedure was completed by a scale categorising UTCI equivalent temperature values in terms of thermal stress, and by providing simplified routines for fast but sufficiently accurate calculation, which included look-up tables of pre-calculated UTCI values for a grid of all relevant combinations of climate parameters and polynomial regression equations predicting UTCI over the same grid. The analyses of the sensitivity of UTCI to humidity, radiation and wind speed showed plausible reactions in the heat as well as in the cold, and indicate that UTCI may in this regard be universally useable in the major areas of research and application in human biometeorology.     

Subjective estimation of thermal environment in recreational urban spaces—Part 1: investigations in Szeged,Hungary

During two investigation periods in transient seasons (14 weekdays in autumn 2009 and 15 weekdays in spring 2010) 967 visitors in two inner city squares of Szeged (Hungary) were asked about their estimation of their thermal environment. Interrelationships of subjective assessments—thermal sensation, perceptions and preferences for individual climate parameters—were analyzed, as well as their connections with the prevailing thermal conditions [air temperature, relative humidity, wind velocity, mean radiant temperature and physiologically equivalent temperature (PET)]. Thermal sensation showed strong positive relationships with air temperature and solar radiation perception, while wind velocity and air humidity perception had a negative (and weaker) impact. If a parameter was perceived to be low or weak, then it was usually desired to be higher or stronger. This negative correlation was weakest in the case of humidity. Of the basic meteorological parameters, Hungarians are most sensitive to variations in wind. Above PET?=?29°C, people usually prefer lower air temperature and less solar radiation. The temperature values perceived by the interviewees correlated stronger with PET, but their means were more similar to air temperature. It was also found that the mean thermal sensation of Hungarians in transient seasons depends on PET according to a quadratic function (R ²?=?0.912) and, consequently, the thermal comfort ranges of the locals differ from that usually adopted.     

Estimating mean monthly incident solar radiation on horizontal and inclined slopes from mean monthly temperatures extremes

Although satellite-borne sensors are now available to estimate cloud cover and incoming short-wave radiation across the Earth’s surface, the study of climatic variation and its impact on terrestrial and marine ecosystems involves historical analyses of data from networks of weather stations that only record extremes in temperatures and precipitation on a daily basis. Similarly, when projections are made with global atmospheric circulation models, the spatial resolution of predicted radiation is too coarse to incorporate the effects of heterogeneous topography. In this paper, we review the development and set forth a set of general equations that allow both diffuse and direct solar radiation to be estimated for each month on the basis of mean daily maximum and minimum temperatures, latitude, elevation, slope, and aspect. Adjustments for differences in slope, aspect, and elevation are made by varying the fraction of diffuse and direct solar beam radiation. To test the equations on various slopes and under different climatic conditions, we drew on high-quality radiation data recorded at a number of sites on three continents. On horizontal surfaces the set of equations predicted both direct and diffuse components of solar radiation within 1%–7% of recorded values. On slopes, estimates of monthly mean solar radiation were with 13% of observed values with a mean error of less than 2 MJ m^–2day^–1 over any given month. Received: 22 October 1999 / Revised: 14 May 2000 / Accepted: 5 June 2000