Photosynthetically Active Radiation Values Research Articles

A Bayesian approach to integrate satellite-estimated instantaneous photosynthetically active radiation product for daily value calculation

[1] Most terrestrial ecology models need daily incident photosynthetically active radiation (PAR) values, but only instantaneous PAR values are directly derivable from remotely sensed data. The conventional interpolation/integration method for estimating daily PAR from instantaneous values is not an optimal choice when only sparsely spaced instantaneous PAR is available. In this study, a method of ratio (MOR) is developed as an alternative, which is proved to provide a more accurate PAR estimation than the interpolation/integration method when the time interval between adjacent instantaneous PAR increases to 3–4 h. Furthermore, a Bayesian MOR is developed to combine the information from instantaneous PAR and existing knowledge of a given location to provide probabilistic estimation of daily PAR based on posterior distribution. The Bayesian MOR models a day's full set of actual-to-maximum instantaneous PAR ratios as a population from a normal process, and it is configured to estimate the joint posterior distribution of the population's mean and variance. The inference of daily PAR is carried out through Monte Carlo simulations based on the joint posterior distribution. Applications to both synthesized ground measurement data and MODIS (Moderate Resolution Imaging Spectroradiometer) derived instantaneous PAR at six Surface Radiation network (SURFRAD) sites demonstrate that the 90% confidence interval inferred from Bayesian MOR successfully includes the actual daily PAR values. Furthermore, sensitivity study demonstrates that sensible changes in prior distribution only have insignificant impacts on the estimation accuracy of daily PAR based on posterior distribution.

Development of a model for the estimation of photosynthetically active radiation from geostationary satellite data in a tropical environment

This paper presents a model for the estimation of photosynthetically active radiation (PAR) from geostationary satellite data. The model is aimed to estimate the monthly average hourly PAR in a tropical environment. This model represents a physical relation of PAR incident on the earth's surface and satellite-derived earth-atmospheric albedo together with the absorption and scattering coefficients of various atmospheric constituents. The earth-atmospheric albedo was obtained from the Multifunctional Transport Satellite-1R (MTSAT-1R). The absorption of PAR by water vapor, an important process for the tropics, was computed from the ambient temperature and relative humidity. The absorption of PAR by aerosols was estimated by using the visibility data and aerosol optical properties obtained from the Aerosol Robotic Network (AERONET) of NASA in this region. The total column ozone from the Ozone Monitoring Instrument onboard of AURA satellite (OMI/AURA) was used for the estimation of the absorption of PAR by ozone. The model was validated against the monthly average hourly PAR from measurements at four solar radiation measuring stations situated in the tropical environment of Thailand. The values of the monthly average hourly PAR estimated from the model and those obtained from the measurement were in good agreement, with the root mean square error (RMSE) and mean bias error (MBE) of 9.8% and 0.6%, respectively. After the validation, the model was employed to estimate the monthly average hourly PAR over Thailand using a 4-year period of data from MTSAT-1R and other ancillary surface data. Values of the monthly average hourly PAR were presented as maps showing the geographical distribution of PAR. These maps reveal the diurnal and seasonal variation of PAR over the country.

Photosynthetically active radiation retrieval based on HJ-1A/B satellite data

Photosynthetically active radiation (PAR) is essential for plant photosynthesis and carbon cycle, and is also important for meteorological and environmental monitoring. To advance China’s disaster and environmental monitoring capabilities, the HJ-1A/B satellites have been placed in Earth orbit. One of their environmental monitoring objectives is the study of PAR. We simulated direct solar, scattered and environment radiation between 400 and 700 nm under different atmospheric parameters (solar zenith angle, atmospheric water vapor, atmospheric ozone, aerosol optical thickness, surface elevation and surface albedo), and then established a look-up table between these input parameters and PAR. Based on the look-up table, we used HJ-1A/B aerosol and surface albedo outputs to derive the corresponding PAR. Validation of inversed instantaneous and observed PAR values using HJ-1 Heihe experimental data had a root mean square error of 25.2 W m−2, with a relative error of 5.9%. The root mean square error for accumulated daily PAR and observed values was 0.49 MJ m−2, with a relative error of 3.5%. Our approach improved significantly the computational efficiency, compared with using directly radiation transfer equations. We also studied the sensitivity of various input parameters to photosynthetically active radiation, and found that solar zenith angle and atmospheric aerosols were sensitive PAR parameters. Surface albedo had some effect on PAR, but water vapor and ozone had minimal impact on PAR.

Hysteresis response of daytime net ecosystem exchange during drought

Abstract. Continuous measurements of net ecosystem CO2 exchange (NEE) using the eddy-covariance method were made over an agricultural ecosystem in the southeastern US. During optimum environmental conditions, photosynthetically active radiation (PAR) was the primary driver controlling daytime NEE, accounting for as much as 67 to 89% of the variation in NEE. However, soil water content became the dominant factor limiting the NEE-PAR response during the peak growth stage. NEE was significantly depressed when high PAR values coincided with very low soil water content. The presence of a counter-clockwise hysteresis of daytime NEE with PAR was observed during periods of water stress. This is a result of the stomatal closure control of photosynthesis at high vapor pressure deficit and enhanced respiration at high temperature. This result is significant since this hysteresis effect limits the range of applicability of the Michaelis-Menten equation and other related expressions in the determination of daytime NEE as a function of PAR. The systematic presence of hysteresis in the response of NEE to PAR suggests that the gap-filling technique based on a non-linear regression approach should take into account the presence of water-limited field conditions. Including this step is therefore likely to improve current evaluation of ecosystem response to increased precipitation variability arising from climatic changes.

Estimation of daily-integrated PAR from sparse satellite observations: comparison of temporal scaling methods

Incident Photosynthetically Active Radiation (PAR) is a critical parameter for modelling ecosystem productivity. An algorithm for estimating instantaneous PAR from Moderate Resolution Imaging Spectroradiometer (MODIS) data was developed earlier; however, daily-integrated PAR is more meaningful than instantaneous PAR in many cases because many land surface models require a daily or coarser temporal resolution. This paper compares two different algorithms (adjusted sinusoidal interpolation and look-up table) for estimating daily-integrated PAR from instantaneous PAR values. Statistical analysis of the validation results indicates that the look-up table method more accurately estimates daily-integrated PAR than the use of adjusted sinusoidal interpolation. We also investigated how window size, daytime length and the number of overpass counts per day affect bias and the relative error of estimation. Validation using field measurements, and comparison with the Geostationary Operational Environmental Satellites PAR product, demonstrates that data collected by MODIS can be used to provide reliable estimates of daily-integrated PAR.

LIGHT ENVIRONMENT WITHIN MATURE RABBITEYE BLUEBERRY CANOPIES INFLUENCES FLOWER BUD FORMATION

LIGHT ENVIRONMENT WITHIN MATURE RABBITEYE BLUEBERRY CANOPIES INFLUENCES FLOWER BUD FORMATION

Benthic primary productivity on the Georgia midcontinental shelf: Benthic flux measurements and high‐resolution, continuous in situ PAR records

Continuous, 7 year records of above‐water, near‐surface water column and near‐bottom measurements of photosynthetically active radiation (PAR) were used in conjunction with in situ chamber measurements to estimate magnitude and seasonal variations in benthic primary productivity (BPP) on the Georgia continental shelf. Correlation between BPP and PAR flux was established with 19 light/dark benthic chamber and PAR flux measurements at water depths from 14 to 40 m. No substantial improvement in the relationship is observed by inclusion of benthic chlorophyll biomass and water temperature, apparently because variations in benthic chlorophyll concentrations are moderated by physical mixing processes and seasonal temperature ranges are relatively modest. Best fit for the data set is described by a simple power function [mg carbon fixed m−2 d−1 = 132(mol photon m−2 d−1)1.45]. In situ, continuous PAR measurements indicate temporal variations and seasonal trends not revealed by previous ship‐based measurements. Importantly, calculations of PAR flux and resulting BPP are significantly less than earlier estimates of benthic PAR derived via local insolation and water column light attenuation from ship‐based light profiling. Furthermore, benthic PAR flux based on continuous above‐water and near‐surface in‐water PAR measurements fails to correctly reflect seasonal trends for near‐bottom PAR. Analysis of the time series data suggests that estimates of the vertical attenuation coefficient for PAR (kPAR) values from ship‐based measurements are biased to calmer conditions while variations in the vertical profile of light attenuation prevent accurate estimates of benthic PAR from near‐surface or above‐water measurements. Accurate estimates of the benthic light field and BPP over the annual cycle require in situ, continuous, high‐resolution near‐bottom measurements provided by ocean observatories.

Modelling potential habitat of the invasive ctenophore Mnemiopsis leidyi in Aegean Sea

The invasive ctenophore Mnemiopsis leidyi was accidentally introduced into the Black Sea in the early 1980s and it was first sighted in the Aegean Sea (Eastern Mediterranean) in the early 1990s. This article presents a first attempt to develop a predictive spatial model based on M. leidyi presence data and satellite environmental data from the Aegean Sea during early summer, in order to identify those areas in the Greek Seas and the entire Mediterranean basin that could serve as potential habitat for the species. Generalized additive models (GAM) were applied. The final GAM model indicated higher probability of finding M. leidyi present in depths of 65–135 m and sea surface temperature values of 21–25°C. Furthermore, the significant interaction between photosynthetically active radiation (PAR) and sea level anomaly (SLA) indicated a higher probability of M. leidyi presence in low values of PAR and SLA. In the next step, the final GAM was applied in a prediction grid of mean monthly satellite values for June 2004–2006 in order to estimate probability of M. leidyi presence in the Hellenic Seas and the whole Mediterranean basin at a GIS resolution of 4 km. In the Aegean Sea, species potential habitat included areas influenced by the Black Sea Water (e.g. Thracian Sea, Limnos-Imvros plateau), gulfs that are affected by river runoffs, such as the Thermaikos, Strymonikos and Patraikos gulfs, or areas with strong anthropogenic influence such as the Saronikos gulf. Areas with the same environmental conditions as those in Aegean Sea have been indicated in certain spots of the Levantine Sea as well as in coastal waters of Egypt and Libya, although their spatial extent varied largely among years examined. However, the occurrence of conditions that are linked to high probability of M. leidyi presence does not necessarily mean that these areas can support successful reproduction, high population or bloom levels, since these depend on a combination of temperature, salinity, food availability and the abundance of predators.

Estimation of Incident Photosynthetically Active Radiation from GOES Visible Imagery

Abstract Incident photosynthetically active radiation (PAR) is an important parameter for terrestrial ecosystem models. Because of its high temporal resolution, the Geostationary Operational Environmental Satellite (GOES) observations are very suited to catch the diurnal variation of PAR. In this paper, a new method is developed to derive PAR using GOES data. What makes this new method distinct from the existing method is that it does not need external knowledge of atmospheric conditions. The new method retrieves both atmospheric and surface conditions using only at-sensor radiance through interpolation of time series of observations. Validations against ground measurement are carried out at four “FLUXNET” sites. The values of RMSE of estimated and ground-measured instantaneous PAR at the four sites are 130.71, 131.44, 141.16, and 190.22 μmol m−2 s−1, respectively. At the four validation sites, the RMSE as the percentage of estimated mean PAR value are 9.52%, 13.01%, 13.92%, and 24.09%, respectively; the biases are −101.54, 16.56, 11.09, and 53.64 μmol m−2 s−1, respectively. The independence of external atmospheric information enables this method to be applicable to many situations in which external atmospheric information is not available. In addition, topographic impacts on surface PAR are examined at the 1-km resolution at which PAR is retrieved using the GOES visible band data.

Mapping incident photosynthetically active radiation from MODIS data over China

Photosynthetically active radiation (PAR) is a key input parameter for almost all terrestrial ecosystem models, but the spatial resolution of current PAR products is too coarse to satisfy regional application requirements. In this paper, we present an operational system for PAR retrieval from MODIS data that is based on an idea proposed by [Liang, S., Zheng, T., Liu, R., Fang, H., Tsay, S. -C., & Running, S. (2006). Estimation of incident photosynthetically active radiation from Moderate Resolution Imaging Spectrometer data. Journal of Geophysical Research, 111, D15208. doi:10.1029/2005JD006730]. However, the operational system for PAR retrieval described here contains several improvements. The algorithm utilizes MODIS 1B data combining MODIS land surface products and BRDF model parameters products to directly estimate diffuse PAR, direct PAR and total PAR. Times-series data interpolation removes the noise and cloud contamination of land surface reflectance. PAR is retrieved by searching look-up tables calculated using a radiative transfer model. The system can automatically process MODIS 1B data to generate instantaneous and daily PAR. The instantaneous PAR products are compared with observational data from seven ChinaFLUX stations, and daily total PAR estimates are compared with those estimates of global radiation from 98 meteorological stations over China. The results indicate that this approach can produce reasonable PAR estimates, although this method overestimates PAR for low values of PAR.

낙엽수(신갈나무)로부터 배출되는 이소프렌 배출속도 측정 연구

The standard emission rate(ERs) of isoprene was quantitatively measured in situ from Quercus mongolica Fischer that dominates more than about 85% of domestic oak trees. The ERs values in spring and summer were similar to 64.4 and 58.1 (), respectively. The ERs in autumn, 7.06(), was about times lower than those in spring and summer. The coefficient of determination () between ERs and ranged from 0.593 to 0.836. The correlation coefficients between the ERs and PAR. the ER and temperature suggested that ERs have strong correlation with PAR(photosynthetically active radiation) and temperature. In addition, the high values of PAR, temperature, and ERs were found in the time zone of (spring), (summer), and (autumn).

Estimation of incident photosynthetically active radiation from Moderate Resolution Imaging Spectrometer data

Incident photosynthetically active radiation (PAR) is a key variable needed by almost all terrestrial ecosystem models. Unfortunately, the current incident PAR products estimated from remotely sensed data at spatial and temporal resolutions are not sufficient for carbon cycle modeling and various applications. In this study, the authors develop a new method based on the look‐up table approach for estimating instantaneous incident PAR from the polar‐orbiting Moderate Resolution Imaging Spectrometer (MODIS) data. Since the top‐of‐atmosphere (TOA) radiance depends on both surface reflectance and atmospheric properties that largely determine the incident PAR, our first step is to estimate surface reflectance. The approach assumes known aerosol properties for the observations with minimum blue reflectance from a temporal window of each pixel. Their inverted surface reflectance is then interpolated to determine the surface reflectance of other observations. The second step is to calculate PAR by matching the computed TOA reflectance from the look‐up table with the TOA values of the satellite observations. Both the direct and diffuse PAR components, as well as the total shortwave radiation, are determined in exactly the same fashion. The calculation of a daily average PAR value from one or two instantaneous PAR values is also explored. Ground measurements from seven FLUXNET sites are used for validating the algorithm. The results indicate that this approach can produce reasonable PAR product at 1 km resolution and is suitable for global applications, although more quantitative validation activities are still needed.

Radiação solar em ambiente protegido cultivado com tomateiro nas estações verão-outono do Rio Grande do Sul

O crescimento e desenvolvimento de uma planta dependem da intensidade, qualidade e duração da radiação solar. Por esse fator ser de importância vital às plantas, o presente trabalho objetivou fazer uma avaliação sobre sua variação, bem como sobre a sua disponibilidade no interior do ambiente protegido durante o ciclo do tomateiro nas estações verão-outono em Pelotas, Rio Grande do Sul. O experimento foi conduzido de janeiro a junho de 2003 no Campus da Universidade Federal de Pelotas (latitude 31°52'S; longitude 52°21'W e altitude de 13m), em estufa plástica disposta no sentido Leste-Oeste, com área de 180m². A cultivar utilizada foi "Flora-dade", semeada em 24/01/03, transplantada no dia 28/02/03, sendo a última colheita em 12/06/03. Avaliou-se a radiação solar global externa (Rgext) e interna (Rgint), transmitância, radiação fotossinteticamente ativa (RFA) e o albedo da cultura a partir de sensores eletrônicos conectados a um "datalloger". Durante o ciclo da cultura, o total de Rgext foi 1161,21MJ m-2, enquanto a Rgint foi 881,85MJ m-2. A Rgint e a RFA apresentaram valores médios diários de 8,5MJ m-2 dia-1 e 3,4MJ m-2 dia-1, respectivamente. A transmitância média da cobertura plástica à radiação solar global foi de 76%. O albedo médio diário da cultura foi 0,23, com albedo de 0,17 nos estádios iniciais, 0,26 no período de máximo crescimento e 0,23 no final do ciclo.

Lycopene content and colour of ripening tomatoes as affected by environmental conditions

AbstractTomatoes may have a great impact in the prevention of some types of cancer. This protective effect has been attributed to lycopene. The biosynthesis of lycopene is affected by environmental conditions. If the temperature of the fruits exceeds 30 °C, the synthesis of lycopene is inhibited. Strong direct radiation on fruits (∼2990 µmol m−2 s−1 for 1.5–4 h) is harmful. In 2002, we investigated the effect of temperature and photosynthetically active radiation (PAR) on lycopene content. Fruit samples were harvested three times during the growing phase. The average lycopene content of harvested fruits, picked on 18 June 2002, reached 64.9 mg kg−1 of fresh tomato. The fruits gathered on 25 June 2002 contained on average only 35.5 mg of lycopene per kilogram. The average lycopene content from the third harvest (on 9 July 2002) was 68.9 mg kg−1. The values of PAR varied between 150 and 415 µmol m−2 s−1, so they did not exceed the critical value. The average temperature preceding the second harvest was the highest (28–32 °C) and the maximum temperature ranged between 40 and 43 °C. This prolonged, extremely high temperature may have caused the low lycopene level in the second harvest. The lycopene content of six ripeness stages, from green to deep red stage, was measured in 2002 and 2003. The accumulation of lycopene accelerates from the pink stage and there is a high correlation (R2 = 0.92) between lycopene content and colour values (a*/b*). The higher the ratio of a*/b*, the higher was the lycopene content. Copyright © 2005 Society of Chemical Industry

(320) Influence of Light Microclimate on the Growth, Yield, and Fruit Quality of Apple

Influence of photosynthetically active radiation (PAR) microclimate in the canopy of four training systems [open-center with high trunk (OH); open-center with middle trunk (OM); open-center with low trunk (OL); and a traditional round canopy (RC)] on the growth, yield and fruit quality of apple were studied in the Beijing area. The results showed that: 1) the growth and yield potential were affected by canopy light microclimate. The average leaf chlorophyll content from OH, OM and OL systems was 12.3% to 18.1% greater than that from the RC system. Trees from OH, OM, and OL systems produced 84.2% to 89.7% of shoot forming flower clusters compared to only 47.3% to 50.9% of the RC shoots. Training system did not affect total yield of 8-year-old trees, but in 10-year-old trees the RC system had lower yields compared with open-center systems. 2) Fruit quality was also affected by canopy light microclimate. The average anthocyanin content in the skin of fruit from OH, OM, and OL systems was 35.9% to 46.1% higher than that from the RC system, but chlorophyll content from the OL system was higher than in the open-center systems. Meanwhile, the contents of TSS and esters in apple flesh from the open-center systems were significantly higher than that from the RC system. 3) When the relative value of PAR in canopy exceeded 33.8%, the growth index of trees (chlorophyll: return-bloom ratio) exceeded 66.6% and the fruit quality index (TSS × anthocyanin) exceeded 94.7%. When PAR was less than 20.6%, the growth index was under 37.2% and the fruit quality index was under 67.5%. PAR value was significantly correlated with the growth and fruit quality index in the four training systems, and the total canopy volume of higher PAR(exceeding 33.8%, relative value) from OH, OM, and OL systems was 37.1% to 45.0% greater than that from the RC system.

Midday values of gross CO 2 flux and light use efficiency during satellite overpasses can be used to directly estimate eight-day mean flux

Most satellites provide, at best, a single daily snapshot of vegetation and, at worst, these snapshots may be separated by periods of many days when the ground was obscured by cloud cover. Since vegetation carbon exchange can be very dynamic on diurnal and day-to-day timescales, the limited temporal resolution of satellite data is a potential limitation in the use of these data to estimate integrated CO 2 exchange between vegetation and the atmosphere. Our objective in this study was to determine whether consistent relationships exist between midday carbon flux on clear days and daily or 8-day mean values. CO 2 flux data were obtained from eight sites, covering a wide range of vegetation types, which are part of the AmeriFlux system. Midday gross CO 2 exchange was highly correlated with both daily and 8-day mean gross CO 2 exchange and these relationships were consistent across all the vegetation types. In addition, it did not make any difference whether the midday data were derived from the AM or PM satellite overpass times, indicating that midday depression of photosynthesis was not a significant factor in these relationships. Inclusion of cloudy days in the 8-day means also did not affect the relationships relative to single clear days. Although there was a relationship between photosynthetic rates and photosynthetically active radiation (PAR) for half hour data, this relationship tended to saturate at PAR values less than half of full sun and for many of the sites the relationship between daily total photosynthesis and PAR was very weak. Consequently, cloudy conditions had less effect on daily gross CO 2 exchange than would have been expected. Conversely, the saturation of photosynthesis at moderate PAR values resulted in considerable variation in light use efficiency (LUE). LUE was higher for daily and 8-day means than it was at midday on clear days and the correlation between midday and 8-day mean LUE was relatively weak. Although these results suggest that it may not be possible to estimate 8-day mean LUE reliably from satellite data, LUE models may still be useful for estimation of midday values of gross CO 2 exchange which could then be related to longer term means of CO 2 exchange.

Mapping PAR using MODIS atmosphere products

Instantaneous PAR (Photosynthetically Active Radiation), computed from atmospheric parameters from individual images from the MODIS sensors aboard the Terra and Aqua satellite platforms, is combined to derive daily integrated PAR and mapped to a local coordinate system. Compared to field observations, the daily integrated PAR values were shown to have average errors in the order of 5–8%, with individual estimation errors as high as 21%, but monthly averages showed much better correspondence with observations yielding averaged absolute errors of around 5%. The error appears to be mostly related to uncertainties in the MODIS aerosol retrieval accuracy. This accuracy and the medium spatial resolution of the PAR map compare very favourably to other sources of PAR data and make this a useful product in the improved assessment of vegetation dynamics.

Changes in Understory Vegetation of a Thinned Japanese Larch (Larix leptolepis) Plantation in Yangpyeong, Korea

Photosynthetically active radiation (PAR) beneath the forest canopy, understory species richness and diversity, and biomass were measured in a Larix leptolepis plantation seven years after thinning in Yangpyeong. Four different thinning intensities (control, <TEX>$10\%,\;20\%\;and\;40\%$</TEX> stocking reduction) were applied in 1997. The current PAR values were lower than those measured four years after thinning, and PAR at the heavy thinning plots was significantly higher than that of other thinning intensities. A total of 23 species including 9 tall-trees and 14 shrubs were found for the high layer while a total of 82 species including 10 tall-trees, 29 shrubs, and 43 herbs for the low layer. Species richness and diversity generally increased with thinning intensities, and the trends were more evident for the low layer. Aboveground biomass significantly differed among thinning intensities for both shrubs and herbs. Also there was a negative correlation between biomass and the current number of stems per hectare. The current study suggested that the effects of thinning on light conditions at the forest floor, species richness and diversity and production of understory vegetation continued seven years after the treatment.

Comparative analysis of the bryophyte vegetation in acidophilous forest communities in the Bükk Mts (NE Hungary)

The bryophyte vegetation of three acidophilous forest communities of four habitats on radiolarian bedrock were investigated in the Bükk Mts. The bryophyte layers of Deschampsio-Fagetum sylvaticae Soó 1962, Genisto pilosae-Quercetum petraeae Zólyomi et al. 1958 and Genisto tinctoriae-Quercetum petraeae Klika 1932 were compared on the basis of the dominance and frequency of 15 bryophyte species in the communities using ordination and cluster analysis methods. The soil pH and the photosynthetically active radiation (PAR) values in the four sampling areas were also compared. The results refer to a strong connection of the bryophyte species composition considering the dominance values and frequency of the species with the community type in different spatial scale. The soil pH values do not differ significantly in the habitats and they refer to a high amount of hidden acidity which is the effect of the radiolarian bedrock type. The PAR values have been statistically analysed and represent the homogeneity or the heterogeneity of the canopy layer and the effect of the exposition. The results show significant difference in the variances of PAR values between Genisto pilosae-Quercetum and the other two community types and the mean PAR value of Deschampsio-Fagetum sylvaticae differ significantly from the mean values of the two Genisto tinctoriae-Quercetum petraeae stands.

Proposal of a function for modelling the hourly frequency distributions of photosynthetically active radiation

Solar irradiance is a key factor in the physiological processes of living beings. To obtain simple correlations for the estimation of the performance of biological systems, which transform the solar energy by photosynthesis, and to generate synthetic data, it is necessary to know the frequency distributions of photosynthetically active radiation (PAR). In this work we carried out an analysis of the properties of hourly values of PAR data, using 9 years of data collected in southern Spain. In particularly, its dependence on the optical mass, for all type of skies including cloudy skies, is studied. Results shows that, for a given value of the optical mass, the PAR density distributions are not symmetrical and have a certain degree of bimodality. The increment in the optical mass value has two effects on the PAR distributions, the first one is a shift toward lower values of the maximum and the second one is a decrease in the range of PAR values. Finally, a model of the frequency distribution of PAR values, based on a new kind of functions related to the Boltzmann’s statistic, is proposed. The parameters of these functions depend just on the optical mass. Results show a very good agreement between the data and the model proposed.