Models of sky radiance distribution and sky luminance distribution

The aim of this research work is to propose sky radiance and luminance distribution models for all sky conditions from clear sky to overcast sky. The classification method of sky conditions is examined. Clear sky index is defined based on the global irradiance. Cloudless index is defined based on the global irradiance and the diffuse irradiance. The sky conditions are classified according to both indices. The data of the average sky radiance (luminance) distributions are obtained based on the classified sky conditions. The average relative sky radiance distributions are compared with the average relative sky luminance distributions. It has been confirmed that both radiance/luminance distributions can be shown by the same equation.An equation that shows the relative sky radiance (luminance) distribution for all sky conditions and equations that show the zenith radiance and the zenith luminance are obtained. The absolute value of the sky radiance (luminance) distribution is shown by multiplying the relative sky radiance (luminance) distribution and the zenith radiance (luminance). The equations to show the absolute values of the sky radiance distribution called the All Sky Model-R and the sky luminance distribution called the All Sky Model-L are proposed.Both models are compared with the previous models based on the measurement distributions concerning the region of sky vault and the sky conditions and good results are obtained. In addition, the vertical irradiance and illuminance calculated by the proposed models and the previous models are compared with the measurements, and the proposed models are confirmed their accuracy.     

Distributions of sky luminance and radiance of North Bangkok under standard distributions

In the tropics, the sky is luminous and variable. Distribution of luminance over the sky dome is non-uniform and varies widely and dynamically with weather condition. The high luminosity offers good potential for daylighting, but an understanding of the luminance distribution of tropical sky would help advance the movement for daylighting. This paper reports results of a characterization of sky luminance and radiance under the standard sky luminance patterns proposed by Kittler using measurements from a station located north of Bangkok. In accordance to the standard sky luminance classification, the sky patterns of north Bangkok mostly fall into clear and intermediate types. During cooler months, the sky is clear for over 60% of the time. In the midst of the rainy season, the sky falls into the intermediate category for over 40% of the time. The high incidence of clear sky on this classification differs from earlier results that use sky ratio and Perez's clearness indices in the classification of sky condition.     

Comparison of four luminance and radiance angular distribution models for radiance estimation

A renewed interest in considering solar energy in the design process of new buildings has favoured the development of simulation software that estimate available solar energy so as to contribute to natural lighting and energy production. The input data required by this type of software are information regarding luminance or radiance angular distribution over the sky dome. However, such information is recorded at a handful of locations being therefore necessary to use estimated values. To that purpose, several models have been developed for both luminance and radiance estimation. In this paper four of these models are analysed and their ability to estimate radiance values is validated using data recorded at two different locations. For some of the models, different versions are considered. In addition, the effect of different data calibration procedures on model performance was investigated. On the whole, it can be concluded that results obtained by the four models are quite similar. However, depending on the version applied or the sky condition analysed, the best performance is derived from different models.     

Synthetic generation of standard sky types series using Markov Transition Matrices

The paper describes a methodology for creating synthetic time series of the fifteen standard sky types considered by the Commission International d'Eclairage (CIE). Since the measurements of sky luminance and accordingly CIE sky types are limited to a small number of locations, it is important to develop models to generate the time series of these parameters. The method is applied to two different locations [Pamplona (Spain) and Arcavacata di Rende (Italy)] where experimental luminance data are available. Firstly, the standard sky types corresponding to the observed luminance values are determined every 10 min and from these, Markov's Transition Matrices (MTM) are obtained corresponding to the four seasons. Secondly, it is statistically verified that the process follows a Markov's chain of first order and that it is stationary. Thirdly, obtained MTMs are used as a basis for generating the synthetic series of types of sky. Finally, experimental and synthetic time series are compared for the two locations, exhibiting good fitting results. As a conclusion, it is verified that first order MTM method can be used to generate time series of occurrence of CIE standard sky types, for the two locations. To clarify the general applicability, it should be applied to different locations having different climates and in addition with longer data sets.     

Radiance distribution on densely overcast skies: comparison with cie luminance standard

In this contribution some data measured in Europe are evaluated to enable the comparison of real radiance distributions with the CIE (International Commission on Illumination) luminance gradation approximation of the densely overcast sky. A question is posed whether such a model sky exists in reality, although the frequency of its occurrence might be different in different seasons and in regions with different climates. Eleven cases are evaluated in Figs. 1–3 with the comparison to the cosine and the exponential approximation curves. It seems that the measurement data agree with the CIE Standard but further tests and results obtained during the International Daylight Measurement Programme have to gather more evidence.     

HOLIGILM: Hollow light guide interior illumination method – An analytic calculation approach for cylindrical light-tubes

A physical model for interior illuminance calculation HOLIGILM applied to cylindrical skylights was developed. Based on the ray-tracing between the diffuser of a tubular skylight and the sky vault including the Sun, the light transmission coefficient of the cover dome and of the interior diffuser with the high light-guide reflection, as well as taking into account the geometry of the interior, the resulting illuminance of the working plane can be analysed. As the model is strictly physical it allows to study influences of optical properties of tubular skylights (dome, tube and diffuser) on the interior daylight illuminance distribution specifying the luminance distribution on the hollow light-guide diffuser. The standard sky luminance distributions adopted ISO 15469:2004 and the new solar luminance and constant were included into the evaluation concept of tubular skylight. In addition to the original formulae some practical examples of the predicted illuminance on the working plane are also presented in this paper.     

An analysis of luminous efficacies under the CIE standard skies

Designing a building to integrate daylight requires an accurate estimation of the amount of available outdoor illuminance. The common method for predicting daylight has been the derivation of illuminance from the more widely measured solar irradiance using the luminous efficacy approach. Recently, the International Commission on Illumination (CIE) has adopted a range of 15 standard skies which cover the whole probable spectrum of skies in the world. This paper presents the work to model the luminous efficacy of diffuse component under the 15 CIE standard skies. Sky luminance distributions measured between 1999 and 2005 were used for the standard sky classifications. An approach to develop luminous efficacy for inclined surfaces was proposed. The predicted vertical outdoor illuminance data for the four cardinal planes (i.e., N, E, S and W) using the proposed luminous efficacy were evaluated against data measured in 2004. Statistical analysis indicated that the estimated daylight illuminance data give acceptable agreements with measured data for all vertical planes.     

Some qualities of scattering functions defining sky radiance distributions

The construction of empirical sky models necessary for the diffuse/sky irradiance calculations can respect theory and reality better when presuming the primary functional influences of the gradation and scattering redistribution of solar radiation within the atmosphere. The multiple scattering/diffusion and reflection caused by tiny particles of the, more or less, turbid atmosphere form the sky pattern which can be characterized by a radiance/luminance solid or its section, the scattering indicatrix. Model approximations of indicatrix functions are analyzed by using theoretical considerations or by deriving indicatrices from measured radiance sky scans. Advantages of applying the scattering indicatrix concept are documented by the comparison of measured, modelled, and calculated indicatrix courses.     

Estimation of sky luminance in the tropics using artificial neural networks: Modeling and performance comparison with the CIE model

An artificial neural network (ANN) model for estimating sky luminance was developed. A 3-year period (2007–2009) of sky luminance data obtained from measurements at Nakhon Pathom (13.82°N, 100.04°E) and a 1-year period (2008) of the same type of data at Songkhla (7.20°N, 100.60°E), Thailand were used in this study. The ANN model was trained using a back propagation algorithm, based on 2 years data (2007–2008) at Nakhon Pathom for clear, partly cloudy and overcast skies. The trained ANN model was used to predict sky luminance at Nakhon Pathom for the year 2009 for the case of clear, partly cloudy and overcast skies. The results were compared with those of the CIE model. It was found that the ANN model performed better than CIE models for most cases. The ANN model trained with Nakhon Pathom data were also used to predict sky luminance at Songkhla and satisfactory results were obtained.     

Development of synthetic hemispheric projections suitable for assessing the sky view factor on vertical planes

The solar radiation balance in buildings has a significant impact on their energy needs, as well as on their potential BIPV energy production. It also influences the potentials of daylight, its healthiness and sustainability. Solar radiation models for urban environments require the characterization of the obstruction degree to which each point is subjected due to other buildings, topography, vegetation, etc. This characterization is carried out with the parameter known as sky view factor (SVF). In this paper, we deepen and extend the study of SVF on vertical surfaces that have a high level of obstruction. This paper aims to present a general mathematical method to obtain projection equations in vertical planes, which allow the study of SVF as a surface ratio. It is also proposed an adequate projection for vertical planes under the hypothesis of angular distribution of diffuse radiance based on Moon-Spencer’s model.     

A COMPREHENSIVE MODEL OF LUMINANCE, CORRELATED COLOUR TEMPERATURE AND SPECTRAL DISTRIBUTION OF SKYLIGHT: COMPARISON WITH EXPERIMENTAL DATA

This study presents the results given by 51 series of 77 spectral directional measurements of sky radiance, taken under various sky conditions, in Lyon, France (lat: 45°78 N, long: 4°93 E, alt: 170 m). The analysis focuses on the relationship between the luminance of any point in the sky and its correlated colour temperature. It is shown that the spatial and spectral distribution of light on the sky vault can be obtained by combining: (1) a sky luminance distribution model — the ASRC-CIE Perez model was used here as an example, (2) a relationship between luminance and correlated colour temperature — a model was developed through this work, and (3) a model to derive the spectrum of daylight from its correlated colour temperature — the CIE method was used in this study.     

Sky luminance/radiance model with multiple scattering effect

Angular distribution of the diffuse light essentially varies with the physical state of a disperse media. The main factors influencing the optical behaviour of the Earth’s atmosphere are the total optical thickness, the scattering ability of atmospheric layers, and also the reflectance of underlying surface. Any model aspiring to be more universal and still satisfactory accurate must at least account for these quantities. The paper presents the theoretically derived equation simulating the sky luminance/radiance under various meteorological conditions. Because the radiative transfer equation in plan-parallel atmosphere is solved exactly, the proposed approximation formula is physically well-founded. Compared with other, predominately empirical models, the presented approach accepts the basic principles of light scattering in a turbid environment and the model is spectral in its nature (contrary to empirical models in current use). In addition, the contribution of multiple scattering is taken into account. A set of free parameters, otherwise used as weighting factors for individual optical effects, makes the model easily scalable and applicable for a wide range of optical states of the atmosphere.     

Predicting daylight illuminance on inclined surfaces using sky luminance data

Daylight illuminance, particularly on vertical surfaces, plays a major role in determining and evaluating the daylighting performance of a building. In many parts of the world, however, the basic daylight illuminance data for various vertical planes are not always readily available. The usual method to obtain diffuse illuminance on tilted planes would be based on inclined surfaces models using data from the horizontal measurements. Alternatively, the diffuse illuminance on a sloping plane can be computed by integrating the luminance distribution of the sky ‘seen’ by the plane. This paper presents an approach to estimate the vertical outdoor illuminance from sky luminance data and solar geometry. Sky luminance data recorded from January 1999 to December 2001 in Hong Kong and generated by two well-known sky luminance models (Kittler and Perez) were used to compute the outdoor illuminance for the four principal vertical planes (N, E, S and W). The performance of this approach was evaluated against data measured in the same period. Statistical analysis indicated that using sky luminance distributions to predict outdoor illuminance can give reasonably good agreement with measured data for all vertical surfaces. The findings provide an accurate alternative to determine the amount of daylight on vertical as well as other inclined surfaces when sky luminance data are available.     

Performance validation of MURAC,a cloudless sky radiance model proposal

The behaviour of a new model, previously proposed, for the directional distribution of the clear sky diffuse radiance is presented in this work. This new model, called MURAC, includes two parameters for which simple expressions without local dependence were proposed. In this way MURAC claims to be a general applicability model for the angular distribution of cloudless sky radiance. We present the model performance analysis by means of the well-known SKYSCAN 83/84 DATA SET, which involves angular sky radiance distributions recorded at Toronto, Canada. This analysis indicates that MURAC is able to estimate instantaneous sky radiance values with a mean bias error of −3.7% and a root mean square error of 63.6%. These results, in the same order of magnitude as other sky radiance models, seem to confirm our expectation.     

Analysis of sky luminance experimental data and comparison with calculation methods

Data of sky luminance measured in Osaka (Japan) and in Arcavacata di Rende (Italy) during a year were analysed and compared with the values predicted by the Perez, Igawa and CIE calculation methods. The best predictions of absolute, relative and zenith luminances were obtained by the CIE method. If the measured luminances in a locality are not available, only by the Perez and the Igawa method is possible to predict the sky luminance distribution under different meteorological conditions. Of these two methods, the Igawa method appears to be more accurate for the prediction of the absolute luminance, and the Perez method for the predictions of the relative luminance.It should be stressed that, before comparison with the calculation models, the sky luminances measured in each scanning have to be corrected in order to make the horizontal illuminance obtained by integration of the luminances on the sky vault equal to the value of the horizontal illuminance measured by photometers. If such a correction is not made owing to the absence of this latter measurement, the errors of the predictions obtained by the models become larger, but they can be reduced by applying a new methodology proposed by the authors.     

Predicting solar irradiance on inclined surfaces using sky radiance data

The availability of more comprehensive solar irradiance data is invaluable for the reduction of cooling load in buildings and for the evaluation of the performance of photovoltaic plants. In many parts of the world, however, the basic solar irradiance data are not always readily available. This paper presents an approach to calculate the solar irradiance on sloped planes by integrating the sky radiance distribution. Sky radiance data recorded from January 1999 to December 2001 in Hong Kong were used to estimate the solar irradiance for the horizontal and four principal vertical surfaces (N, E, S and W). The performance of this approach was assessed against data measured in the same period. Statistical results showed that using sky radiance distributions to predict solar irradiance can give reasonably good agreement with measured data for both horizontal and vertical planes. The prediction approach was also employed to compute the solar irradiance of a 22.3° (latitude angle of Hong Kong) inclined south oriented surface. The findings indicated that the method can provide an accurate alternative to determine the amount of solar irradiance on inclined surfaces facing various orientations when sky radiance data are available.     

Angular distribution of clear sky short wavelength radiance

Over 3000 scans of the clear sky short wavelength (0.3–3.0 μm) radiance were used to produce sky radiance contour maps for solar zenith angles 32° to 80°. The radiance contours are symmetrical about the solar meridian with minimum radiance in the solar meridian at approximately 90° to 110° from the sun. There is no significant change in contour for a change in aerosol optical depth from 0.1 to 0.5. The clear sky radiance is given analytically by N(ψ) = (1.63 + 53.7e−5.49ψ + 2.04 cos² ψ cos θ^*) (1 − e^{−1.90 sec θ}) (1 − e^{−0.53 sec θ}*) where θ^* is the solar zenith angle, θ the zenith angle of the sky radiance direction, and Ψ is the scattering angle between sky and sun directions.     

Intra-hour forecasting with a total sky imager at the UC San Diego solar energy testbed

A method for intra-hour, sub-kilometer cloud forecasting and irradiance nowcasting using a ground-based sky imager at the University of California, San Diego is presented. Sky images taken every 30 s were processed to determine sky cover using a clear sky library and sunshine parameter. From a two-dimensional cloud map generated from coordinate-transformed sky cover, cloud shadows at the surface were estimated. Limited validation on four partly cloudy days showed that (binary) cloud conditions were correctly nowcast 70% of the time for a network of six pyranometer ground stations spread out over an area of 2 km². Cloud motion vectors were generated by cross-correlating two consecutive sky images. Cloud locations up to 5 min ahead were forecasted by advection of the two-dimensional cloud map. Cloud forecast error increased with increasing forecast horizon due to high cloud cover variability over the coastal site.     

Investigation of the validity of the TDRC model for the distribution of diffuse sky radiance

The validity is investigated of the three discrete radiance components (TDRC) model, which was introduced by the author as a model for the instantaneous and time-averaged distribution of diffuse sky radiance. The TDRC model incorporates the cloudy sky geometry (CSG) model, a model proposed by the author for the distribution of clouds across the sky dome in which clouds are modelled as upright vertical cylinders of variable diameter and height, and in which the distribution of clouds is modelled as cylinders randomly spaced, but having an average separation distance in any azimuthal direction. The investigation involves a calibration of the TDRC model for the case of cumulus clouds, followed by a validation under time-averaged conditions of the calibrated model, in which predictions of the model are compared with luminance observations, for a wide range of cloudiness. This comparison showed good agreement, and supports the validity of the TDRC model. It is anticipated that the TDRC model will be of significance to researchers in several fields, particularly those in solar engineering.     

Computational derivation of irradiance on building surfaces: An empirically-based model comparison

Performance simulation applications require reliable information regarding the intensity of solar irradiance on arbitrarily oriented building surfaces in order to properly predict buildings' energy use or to configure building-integrated solar energy systems. Since measured irradiance databases typically include only horizontal irradiance values, solar radiation intensity on inclined surfaces must be computationally derived. In this context, the present paper compares six options to derive, from horizontal irradiance data, solar radiation intensity levels on inclined surfaces. To evaluate these options, simulated downward vertical irradiance on four orientations were compared with measurements obtained in Austria. Two options that use both global and diffuse horizontal irradiance values for sky radiance generation delivered slightly better results than the others, which require only global horizontal irradiance. However, the range of errors was rather high for all options. Even for the best-ranked option, no more than 64% of the results had a relative error of less than ±20%.