Ultraviolet sky radiance distributions of translucent overcast skies

Summary The diffuse sky radiation component in the ultraviolet wavelengths is often at least 50% of the global irradiance under clear skies, and is the dominant component of ultraviolet global radiation under translucent overcast skies. The distribution of sky radiance was measured in a rural area and modeled for wavelength bands of ultraviolet-B (UVB, 280–320 nm) and ultraviolet-A (UVA, 320–400 nm). Sky radiance measurements were made during the summer of 1993 over a wide range of solar zenith angles using radiance sensors mounted on a hand-operated hemispherical rotation mount. UVB irradiance measurements were also made during each scan. Since the ratio of measured irradiance under overcast skies and that predicted for clear skies was not correlated with cloud base height, opaque cloud fraction, or solar zenith angle, it was concluded that the scattering from the clouds dominated the global irradiance, and this scattering was relatively unaffected by the scattering off opaque clouds in the translucent atmosphere.Analysis of the translucent overcast sky UVA and UVB radiance measurements using a semi-empirical distribution model showed that the spectral influences on multiple scattering, single scattering, and horizon brightening components of the distributions agreed with basic atmospheric radiation theory. The best model used solar zenith, the sky zenith, and the scattering angle with resultant coefficient of determination values of 0.62 and 0.25 for the UVA and UVB respectively. The developed equations can be applied directly to the diffuse sky irradiance on the horizontal to provide radiance distributions for the sky.With 6 Figures     

Parameterisation of incoming longwave radiation over glacier surfaces in the semiarid Andes of Chile

A good understanding of radiation fluxes is important for calculating energy, and hence, mass exchange at glacier surfaces. This study evaluates incoming longwave radiation measured at two nearby glacier stations in the high Andes of the Norte Chico region of Chile. These data are the first published records of atmospheric longwave radiation measurements in this region. Nine previously published optimised parameterisations for clear sky emissivity all produced results with a root mean square error (RMSE) ~20 W?m^?2 and bias within ±5 W m^?2, which is inline with findings from other regions. Six optimised parameterisations for incoming longwave in all sky conditions were trialled for application to this site, five of which performed comparably well with RMSE on daytime data <18 W?m^?2 and bias within ±6 W?m^?2 when applied to the optimisation site and RMSE <20 W?m^?2 and bias within ±10 W m^?2 when applied to the validation site. The parameterisation proposed by Mölg et al. (J Glaciol 55:292-302, 2009) was selected for use in this region. Incorporating the proposed elevation modification into the equation reduced the bias in the modelled incoming longwave radiation for the validation site. It was found that applying the parameterisation optimised in the original work at Kilimanjaro produced good results at both the primary and validation site in this study, suggesting that this formulation may be robust for different high mountain regions.     

Effect of clouds on UV and total irradiance at Paradise Bay, Antarctic Peninsula, from a summer 2000 campaign

Summary ?The analysis of ground-based measurements of solar erythemal ultraviolet (UV) irradiance with a Solar Light 501 biometer, and total (300–3000 nm) irradiance with an Eppley B&W pyranometer at the Argentine Antarctic Base “Almirante Brown”, Paradise Bay (64.9° S, 62.9° W, 10 m a.s.l.) is presented. Measurement period extends from February 16 to March 28 2000. A relatively high mean albedo and a very clean atmosphere characterise the place. Sky conditions were of generally high cloud cover percentage. Clear-sky irradiance for each day was estimated with model calculations, and the effect of the cloudiness was studied through the ratio of measured to clear-sky value (r). Two particular cases were analysed: overcast sky without precipitation and overcast sky with rain or slight snowfall, the last one presenting frequently dense fog. Total irradiance was more attenuated than UV by the homogeneous cloudiness, obtaining mean r values of 0.54 for erythemal irradiance and 0.30 for total irradiance in the first case (without precipitation) and 0.27 and 0.17 respectively in the second case (with precipitation). Mean r values for the complete period were 0.58 for erythemal irradiance and 0.43 for total irradiance. Erythemal and total daily insolations reduce quickly at this epoch due to the increase of the noon solar zenith angle and the decrease of daylight time. Additionally, they were strongly modulated by cloudiness. Measured maxima were 2.71 kJ/m² and 18.42 MJ/m² respectively. Measurements were compared with satellite data. TOMS-inferred erythemal daily insolation shows the typical underestimation with respect to ground measurements at regions of high mean albedo. Measured mean total daily insolation agrees with climatological satellite data for the months of the campaign. Received August 9, 2002; revised January 4, 2003; accepted January 28, 2003 Published online May 20, 2003     

Cloud Transmission Estimates of UV-B Erythemal Irradiance

Summary Two UV-Biometer 501A instruments were used to estimate global erythemal irradiance at two locations in southwest Sweden; the Earth Sciences Centre, University of G?teborg (57.69° N; 11.92° E) and the island of Nordkoster, 200 km to the north (58.83° N; 10.72° E). A semi-empirical radiative transfer model was used to calculate the global erythemally effective irradiance under clear skies. A ratio of the hourly measured to clear-sky modelled irradiance was then derived for zenith angles 35–70°. Subsequent comparisons were then made with routine measurements of sunshine duration at G?teborg and sunshine duration, cloud cover, type and height at Nordkoster. Cloud transmission of UV-B irradiance decreases with increasing solar zenith angle, with cloud attenuation being 8% stronger at Nordkoster Island for zenith angles >>;60°. Transmission also decreases with increasing cloud cover such that overcast cloud conditions reduce transmissions by an average of 75%. In addition, cloud type affects the amount of ground incident irradiant flux. Fractus cloud afforded the least UV-B transmission (0.16), while cirrus filaments afforded the most (0.95). The spatial and temporal distribution of clouds appears tobe non-random. Under conditions of 1 to 3 octas, sky cover, clouds appear to be concentrated in line with the sensor and Sun on more occasions than that expected given a random cloud distribution. The same cloud cover condition also resulted in many instances of ground incident irradiance above clear-sky values. The presence of cumuliform clouds appears to increase the likelihood of the latter phenomena. Received January 4, 1998     

Validation of a method to estimate direct normal irradiance of UVA and PAR bands from global horizontal measurements for cloudless sky conditions in Valencia, Spain, by a measurement campaign

A method is proposed to provide measurement of direct normal solar irradiance of bands with wavelength ranges (315?C400?nm, 400?C700?nm) from measurements of global horizontal band irradiance for cloudless sky conditions in Valencia. Global and normal direct irradiance data for every air mass were obtained by applying the SMART2 model to the atmosphere of Valencia. The direct normal to global irradiance ratio was parameterized versus the relative optical air mass. A measurement campaign of global horizontal and diffuse irradiance of UVA and PAR bands was carried out in Valencia, after which, the inferred direct normal irradiance was compared with those provided by the method. The result of the comparison shows that the method is acceptably accurate. The proposed model tends to underestimate the direct normal irradiance of the UVA band by 6%, although for values below 25?W/m² the model overestimates the direct irradiance by 6%, while for values above 25?W/m² the model underestimates it by 10%. The other two error estimators used ranging from 11% to 15% are similar in the defined interval measurements in relation to the whole UVA band. Regarding the PAR band, the model overestimates the direct normal irradiance of the PAR band by only 2.2%. With this, the results of the PAR band are more conclusive, as it has been found that for direct normal irradiance values higher than 280?W/m² the MBE error is almost zero and the other two estimator errors are small, about 5%.     

Ultraviolet radiation in overcast sky at the surface

Based on the analysis of one year of observation data of solar radiation at the ground in Beijing in 1990, a simple empirical formula for calculating UV radiation in overcast sky is established. The formula is Qlw/Quvo = A1S Ao, where Quv and Quvo are monthly mean daily sums of UV exposure in overcast sky and clear sky, respectively. S is the daily sunshine hours. The calculated results agree well with the observed. The maximum and minimum relative biases are 9.9% and 0.1%, respectively, and the yearly relative bias is 2.9%. The ratio of ultraviolet radiation of overcast sky to clear sky in 1990 is between 44.6% and 61.8%, and the yearly average is 53.9%. Thus, almost half of the UV energy is lost in the atmosphere in overcast sky in 1990.     

Estimating sunshine duration from other climatic data by artificial neural network for ET0 estimation in an arid environment

Sunshine duration data are desirable for calculating daily solar radiation (R _s) and subsequent reference evapotranspiration (ET₀) using the Penman–Monteith (PM) method. In the absence of measured R _s data, the Ångström equation has been recommended by the Food and Agriculture Organization (FAO) of the United Nations. This equation requires actual sunshine duration that is not commonly observed at many weather stations. This paper examines the potential for the use of artificial neural networks (ANNs) to estimate sunshine duration based on air temperature and humidity data under arid environment. This is important because these data are commonly available parameters. The impact of the estimated sunshine duration on estimation of R _s and ET₀ was also conducted. The four weather stations selected for this study are located in Sistan and Baluchestan Province (southeast of Iran). The study demonstrated that modelling of sunshine duration through the use of ANN technique made acceptable estimates. Models were compared using the determination coefficient (R ²), the root mean square error (RMSE) and the mean bias error (MBE). Average R ², RMSE and MBE for the comparison between measured and estimated sunshine duration were calculated resulting 0.81, 6.3 % and 0.1 %, respectively. Our analyses also demonstrate that the difference between the measured and estimated sunshine duration has less effect on the estimated R _s and ET₀ by using Ångström and FAO-PM equations, respectively.     

1/f noise in the UV solar spectral irradiance

The investigation of the intrinsic properties of the solar spectral irradiance as a function of the ultraviolet (UV) wavelength is attempted by exploiting rare observations performed at the Villard St. Pancrace station of the Lille University of Sciences and Technology ranging from 278 to 400 nm with a step of 0.05 nm every half an hour from nearly sunrise to sunset. To achieve this goal, the modern method of the detrended fluctuation analysis was applied on the solar spectral irradiance values versus wavelength. This analysis revealed that the solar incident flux at the top of the atmosphere and the solar spectral irradiance at the ground during two overcast sky days fluctuate with the UV wavelength exhibiting persistent long-range power-law behavior. More interestingly, the exponent of the power-law relationship between the fluctuations of the solar spectral irradiance versus UV wavelength at both the top of the atmosphere and the ground is consistently close to unity (of 1/f-type) throughout the day. This 1/f behavior has been detected in many complex dynamical systems, but despite much effort to derive a theory for its widespread occurrence in nature, it remains unexplained so far. According to the above-mentioned findings we speculate that the 1/f property of the incident solar UV flux at the top of the atmosphere could probably drive both the 1/f behavior depicted in the atmospheric components and the solar UV irradiance at the Earth's surface. The latter could influence the UV-sensitive biological ecosystems, giving rise to a 1/f-type variability in the biosphere, which has already been proven by recent observational data. We finally propose that Wien approximation could be multiplied by a 1/f function of wavelength (e.g., of the type of the fractional Brownian motion) in order to reproduce the aforementioned 1/f feature of the solar UV flux.     

Error assessment of climate variables for FAO-56 reference evapotranspiration

Meteorological stations, which measure all the required meteorological parameters to estimate reference evapotranspiration (ET_o) using the Food and Agriculture Organization Penman?CMonteith (FAO56-PM) method, are limited in Korea. In this study, alternative methods were applied to estimate these parameters, and the applicability of these methods for ET_o estimation was evaluated by comparison with a complete meteorological dataset collected in 2008 in Korea. Despite differences between the estimation and observation of radiation and wind speed, the comparison of ET_o showed small differences [i.e., mean bias error (MBE) varying ?0.22 to 0.25?mm?day^?1 and root-mean-square-error (RMSE) varying 0.06?C0.50?mm?day^?1]. The estimated vapor pressure differed considerably from the observed, resulting in a larger discrepancy in ET_o (i.e., MBE of ?0.50?mm?day^?1 and RMSE of 0.60?C0.73?mm?day^?1). Estimated ET_o showed different sensitivity to variations of the meteorological parameters??in order of vapor pressure?>?wind speed?>?radiation. It is clear that the FAO56-PM method is applicable for reasonable ET_o estimation at a daily time scale especially in data-limited regions in Korea.     

Reconstruction of daily ultraviolet radiation for nine observation stations in China

The aim of this study was to reconstruct daily ultraviolet (UV) radiation (daily cumulation, similarly hereinafter) for nine observation stations in China, using a radiative transfer model combined with empirical relationships. Measurements of global total solar (G) radiation, UV radiation, and their ratio (UV/G) at the nine stations were analyzed for the period 2006–2011. The daily cloud and aerosol attenuation ratios were defined to quantitatively evaluate the effect of cloud and aerosols on radiation, based on measurements and simulated data under cloudless-sky conditions. A semi-empirical reconstruction method for UV radiation was established at each station using cloud modification factors, and by applying an equation that relates G and UV radiation measurements, as well as their corresponding simulations under cloudless conditions. Daily UV radiation values were reconstructed and compared with ground-based measurements for the nine stations, and the results revealed most of the slope values to be close to one, and the determination coefficients ranged from 89.5 to 95.7 %. The values of mean absolute bias error (MABE) and root-mean-square error (RMSE) were below 15 and 18 % for all stations, respectively, and at most stations were even lower than 10 %. A comparison of monthly measured and reconstructed UV radiation for the nine stations was also performed, revealing the values of MABE and RMSE to be even smaller with values of less than 5 %. According to these results, we conclude that the method established in this study has good applicability and transferability.     

基于EC细网格数值预报产品的太阳辐照度订正技术

太阳辐照度与光伏电站发电功率密切相关,其预报的准确性直接影响发电功率预报的准确性。根据光伏电站太阳辐照度实况、气象站实况、WRF(Weather Research and Forecast Model)模式辐照度预报、EC细网格数值预报以及太阳理论辐照度,利用逐步回归法开展太阳辐照度预报订正研究,得到以下结论:①太阳辐照度实况与太阳理论辐照度的比值与EC细网格数值预报中气象要素的相关性优于太阳辐照度实况与气象要素的相关性;②不同时刻影响太阳辐照度的气象因子存在差异,通过逐步回归法建立不同时刻太阳辐照度预报模型;③在非晴天情况下,回归预报辐照度相对均方根误差比WRF模式预报辐照度降低10%左右,减小了辐照度预报误差。该研究成果在光伏电站的新能源数值预报服务中有一定的应用价值。     

Differences between true mean daily, monthly and annual air temperatures and air temperatures calculated with three equations: a case study from three Croatian stations

Differences between true mean daily, monthly and annual air temperatures T0 [Eq. (1)] and temperatures calculated with three different equations [(2), (3) and (4)] (commonly used in climatological practice) were investigated at three main meteorological Croatian stations from 1 January 1999 to 31 December 2011. The stations are situated in the following three climatically distinct areas: (1) Zagreb-Gri? (mild continental climate), (2) Zavi?an (cold mountain climate), and (3) Dubrovnik (hot Mediterranean climate). T1 [Eq. (2)] and T3 [Eq. (4)] mean temperatures are defined by the algorithms based on the weighted means of temperatures measured at irregularly spaced, yet fixed hours. T2 [Eq. (3)] is the mean temperature defined as the average of daily maximum and minimum temperature. The equation as well as the time of observations used introduces a bias into mean temperatures. The largest differences occur for mean daily temperatures. The calculated daily difference value from all three equations and all analysed stations varies from ?3.73 °C to +3.56 °C, from ?1.39 °C to +0.79 °C for monthly differences and from ?0.76 °C to +0.30 °C for annual differences.     

Evaluation of Solar Irradiance Models with a Special Referenceto Globally-Parameterized and Land Cover-Sensitive Solar123

Summary  Numerical models are often the only means available to generate solar irradiance (SR) information, for historical or future SR specifications as well as due to inadequacies of contemporary SR measurements. This paper evaluates five such models that have been proposed as generic and applied as such. Special emphasis is given to Solar123, an integrative model rooted in Lambert’s Cosine Law and Bouguer’s Law with globally-parameterized atmospheric property functions and with input limited to precipitation, air temperature, geographic location, topography and rudimentary land cover information. The selected SR models in general perform well in reproducing the SR data for the USA, with a root mean square error-to-data mean ratio (RMSE/SR_mean ratio) of 9.8–11.4%. A possible exception is the Bristow-Campbell logic as implemented by the Vegetation/Ecosystem Modeling and Analysis Project. Beyond the USA, Solar123 yields an RMSE/SR_mean ratio of 8–17% by region (196 stations in total), generally outperforming the other SR models. Compared to time-sequential monthly SR data, projections by Solar123 have an RMSE/SR_mean ratio of 8.6–14.1% for six weather stations representative of major climate regimes in Canada, or an RMSE/SR_mean ratio of 13–24% for three forest sites in the USA, Germany and Japan. Solar123 projections also compare favorably against the output from the General Circulation Models in terms of ratio change in SR with the doubling of the atmospheric carbon-dioxide concentration: the two fall within ±10% of each other for 85% of a total 264 cases, and within ±20% for all but 3 of the cases. The above statistics suggest that Solar123 represents an improvement over other SR models not only in configuration but also in projection accuracy, and that Solar123 is useful for projecting spatial variation in SR across weather stations around the world and over different land covers, and for projecting temporal variation in SR under the present climate regimes and likely for regimes changed beyond the present fluctuation range. The work further calls into question the common practice of applying SR data irrespective of local land cover. Received May 20, 1999     

Retrospective cloud determinations from surface solar radiation measurements

Surface solar radiation measurements have been made at many meteorological sites for long periods. These data potentially provide higher temporal resolution cloud amount information than traditional estimations of cloud amount recorded in eighths of the sky obscured (oktas). To utilise existing solar radiation datasets for this, two quantities are derived from the surface measurements of global (G) and diffuse (D) solar irradiance, and top of atmosphere solar irradiance (E) — the Diffuse Fraction (DF = D/G) and the Opaqueness (Op = 1 - G/E). These are compared with subjective cloud observations made at Reading daily during 1997 to 2006. This shows that DF measurements are sensitive to cloud amount, particularly for low and moderate cloud coverage. Complimentary information is available in Op, which is particularly sensitive to cloud amount in moderate to overcast cloud coverage. In overcast conditions, DF = 1, during which Op provides a measure of overcast cloud thickness. As well as cloud amount, the variability in DF and Op provides a basis for discriminating between cumuliform and stratiform cloud: large variability indicates convective cloud whereas only small variability occurs under stratiform cloud.     

Classification of daily solar irradiation by fractional analysis of 10-min-means of solar irradiance

Summary This paper deals with fractal analysis of daily solar irradiances measured with a time step of 10 minutes at Golden and Boulder located in Colorado. The aim is to estimate the fractal dimensions in order to perform classification of daily solar irradiances. The estimated fractal dimension and the clearness index KT are used as classification criteria. The results show that these criteria lead to three classes: clear sky, partially covered sky and overcast sky. The results also show that the evaluation of the fractal dimension of the irradiance signal based on a data set with 10 minutes time step is possible.     

The influence of clouds on surface UV erythemal irradiance

The purpose of this study is to examine the effect of clouds on the ultraviolet erythemal irradiance. The study was developed at three stations in the Iberian Peninsula: Madrid and Murcia, using data recorded in the period 2000–2001, and Zaragoza, using data recorded in 2001. In order to determine the cloud effect on ultraviolet erythemal irradiance, we considered a cloud modification factor defined as the ratio between the measured values of ultraviolet erythemal irradiance and the corresponding clear-sky ultraviolet erythemal irradiance, which would be expected for the same time period and atmospheric conditions. The dependence of this cloud modification factor on total cloud amount, cloud type and solar elevation angle was investigated. The results suggest that the effect of cloud on ultraviolet erythemal irradiance can be parameterized in a simple way in terms of the cloud amount. Our results suggest that the same cloud modification factor model can be used at the three analysed locations estimating the ultraviolet erythemal irradiance with mean bias deviation (MBD) in the range of the expected experimental errors. This cloud modification factor is lower than that associated to the whole solar spectral range, indicating that the attenuation for the ultraviolet erythemal irradiance is lower than that associated to other solar spectral ranges. The cloud modification factor for ultraviolet erythemal irradiance presents dependence with solar elevation, with opposite dependencies with solar elevation for overcast and partial cloud cover conditions, a fact that can be explained in terms of the influence of reflection-enhancement of the ultraviolet irradiance in the last case. Concerning the influence of cloud type, a limited study of two cloud categories, low and medium level and high level, indicated that for overcast conditions, lower clouds presents an attenuation of ultraviolet erythemal irradiance 20% greater than that associated to high level clouds.     

Estimation and Projection of Non-Linear Relative Sea-Level Rise in the Seto Inland Sea,Japan

Future sea-level rise (SLR) in and around the Seto Inland Sea (SIS), Japan, is estimated in 2050 and 2100 using ensemble empirical mode decomposition (EEMD) and long-term sea-level records. Ensemble empirical mode decomposition, an adaptive data analysis method, can separate sea-level records into intrinsic mode functions (IMFs) from high to low frequencies and a residual. The residual is considered a non-linear trend in the sea-level records. The mean SLR trend at Tokuyama in the SIS from EEMD is 3.00?mm?y^?1 from 1993 to 2010, which is slightly lower than the recent altimetry-based global rate of 3.3?±?0.4?mm?y^?1 during the same period. Uncertainty in SLR is estimated by considering interdecadal variations in the sea levels. The resulting SLR in 2050 and 2100 for Tokuyama is 0.19?±?0.06?m and 0.56?±?0.18?m, respectively. The stations along the coast of the Pacific Ocean display a greater and more rapid SLR in 2100 compared with other stations in the SIS. The SLR is caused not only by mass and volume changes in the sea water but also by other factors, such as local subsidence, tectonic motion, and river discharge. The non-linear trend of SLR, which is the residual from EEMD, is interpreted as the sum of the local factors that contribute to the sea-level budget.     

The influence of vegetation and building morphology on shadow patterns and mean radiant temperatures in urban areas: model development and evaluation

The solar and longwave environmental irradiance geometry (SOLWEIG) model simulates spatial variations of 3-D radiation fluxes and mean radiant temperature (T _mrt) as well as shadow patterns in complex urban settings. In this paper, a new vegetation scheme is included in SOLWEIG and evaluated. The new shadow casting algorithm for complex vegetation structures makes it possible to obtain continuous images of shadow patterns and sky view factors taking both buildings and vegetation into account. For the calculation of 3-D radiation fluxes and T _mrt, SOLWEIG only requires a limited number of inputs, such as global shortwave radiation, air temperature, relative humidity, geographical information (latitude, longitude and elevation) and urban geometry represented by high-resolution ground and building digital elevation models (DEM). Trees and bushes are represented by separate DEMs. The model is evaluated using 5?days of integral radiation measurements at two sites within a square surrounded by low-rise buildings and vegetation in G?teborg, Sweden (57°N). There is good agreement between modelled and observed values of T _mrt, with an overall correspondence of R ²?=?0.91 (p?<?0.01, RMSE?=?3.1?K). A small overestimation of T _mrt is found at locations shadowed by vegetation. Given this good performance a number of suggestions for future development are identified for applications which include for human comfort, building design, planning and evaluation of instrument exposure.     

Generation of daylight reference years for two European cities with different climate: Athens, Greece and Bratislava, Slovakia

In this work, daylight reference years (DRYs), based on daylight and solar radiation measurements, are designed for two European cities, Athens, Greece and Bratislava, Slovakia, by using the Danish method, the Festa–Ratto technique and the Modified Sandia National Laboratories methodology. The data basis consists of 5-minute values of global and diffuse horizontal illuminance, global and diffuse horizontal irradiance, zenith luminance and solar altitude as well as of daily values of sunshine duration for 5 years for Athens and 8 years for Bratislava. Moreover, Linke's turbidity factor, luminous turbidity factor and relative sunshine duration are calculated and utilized. Then, for each DRY, the predominant sky-luminance distributions over Athens and Bratislava are identified, by using the methodology of Kittler et al., who corresponded the main sky conditions to 15 theoretical sky standards in diagrams of the ratio of zenith luminance to diffuse horizontal illuminance against solar altitude.For both cities the three aforementioned methods do not create identical DRYs. Despite the differences, the sky types defined for each of the two places seem not to depend on the choice of DRY. The predominant sky standard, for all of them, is a cloudless, polluted sky with a broad solar corona for Athens and an overcast sky with slight brightening towards the sun as well as very clear sky with low atmospheric turbidity for Bratislava. However, the selection of the DRY, which represents best the daylight conditions, is necessary for studies in saving energy in buildings. The DRY, which is created by the Modified Sandia National Laboratories method, is chosen for most cases, while the one created by the Danish method is also useful on certain occasions.     

A new approach to identify the sensitivity and importance of physical parameters combination within numerical models using the Lund–Potsdam–Jena (LPJ) model as an example

Daily global solar irradiation (R _s) is one of the main inputs in environmental modeling. Because of the lack of its measuring facilities, high-quality and long-term data are limited. In this research, R _s values were estimated based on measured sunshine duration and cloud cover of our synoptic meteorological stations in central and southern Iran during 2008, 2009, and 2011. Clear sky solar irradiation was estimated from linear regression using extraterrestrial solar irradiation as the independent variable with normalized root mean square error (NRMSE) of 4.69 %. Daily R _s was calibrated using measured sunshine duration and cloud cover data under different sky conditions during 2008 and 2009. The 2011 data were used for model validation. According to the results, in the presence of clouds, the R _s model using sunshine duration data was more accurate when compared with the model using cloud cover data (NRMSE = 11. 69 %). In both models, with increasing sky cloudiness, the accuracy decreased. In the study region, more than 92 % of sunshine durations were clear or partly cloudy, which received close to 95 % of total solar irradiation. Hence, it was possible to estimate solar irradiation with a good accuracy in most days with the measurements of sunshine duration.