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Subdivision of the sky hemisphere for luminance measurements



A scanning pattern for sky photometry is described, in which the hemisphere is divided into 151 zones in bands parallel with the horizon.
... The sky view factor (SVF) was introduced to classify obstructions resulting either from 'self-shadowing' by the slope itself (known as shading) or from adjacent terrain (shadowing) [39]. A procedure to calculate the SVF is suggested in Tregenza [40], where the division of the sky hemisphere into small segments or sky zones is proposed. From this work, the International Commission on Illumination (CIE) recommended the use of a hemisphere evenly-distributed in 145 virtual light sources. ...
... It is written in C language and is included in RADIANCE in the form of a module called GenCumulativeSky. It consists on the scheme based on Tregenza [40] in which each of 145 patches subtends a similar solid angle. The all-weather Perez model [55] is then used to predict the global irradiance at the centroid of these patches. ...
Cityscapes provide a complex environment, where solar radiation is unevenly distributed, especially since urban features started to propagate more and more vertically. Due to the dynamic overshadowing effects present on building surfaces, quantifying these phenomena is essential for predicting reductions in solar radiation availability that can significantly affect potential for solar energy use. Numerical radiation algorithms coupled with GIS tools are a pathway to evaluate those complex effects. Accurate representation of the terrain, vegetation canopy and building structures allows better estimation of shadow patterns. Higher spatial and temporal resolutions deliver more detailed results, but models must compromise between accuracy and computation time. In this paper, models ranging from simple 2D visualization and solar constant methods, to more sophisticated 3D representation and analysis, are reviewed. Web-based solar maps, which rely on the previous features to successfully communicate the benefits of the solar resource to the public and support in the policy-making process, are also addressed.
... The unit was programmed to sample the radiance at intervals of 15 degrees along both spherical coordinates (θ and φ) such that a total of 150 measurements resulted from each scan. Note that our 150-points selection covers a smaller fraction of the sky hemisphere than the Tregenza-based systems [15], which results in a lower spatial resolution. Although we could program additional sampling points for matching the spatial resolution of Tregenza-based systems, this would increase the scanning time lowering the temporal resolution of the system and making it harder to track the effects of fast-moving clouds, for example. ...
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The angular distribution of the sky radiance determines the energy generation of solar power technologies as well as the ultraviolet (UV) doses delivered to the biosphere. The sky-diffuse radiance distribution depends on the wavelength, the solar elevation, and the atmospheric conditions. Here, we report on ground-based measurements of the all-sky radiance at three sites in the Southern Hemisphere across a transect of about 5,000 km: Santiago (33°S, a mid-latitude city of 6 million inhabitants with endemic poor air quality), King George Island (62°S, at the northern tip of the Antarctic Peninsula, one of the cloudiest regions on Earth), and Union Glacier (79°S, a snow-covered glacier in the vast interior of Western Antarctica). The sites were strategically selected for studying the influence of urban aerosols, frequent and thick clouds, and extremely high albedo on the sky-diffuse radiance distribution. Our results show that, due to changing site-specific atmospheric conditions, the characterization of the weather-driven sky radiance distribution may require ground-based measurements.
... The spectral radiance of the sky dome is also given in .txt file format for 145 Tregenza sky patches [9]. For the evaluation of the light distribution, LUMOS can create calculation metrics, such as points and areas, as well as daylight factor (DF) points, which give the percentage of indoor daylight compared to unobstructed outdoor daylight [10]. ...
Conference Paper
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LUMOS is a spectral radiosity simulation tool developed for lighting research applications in MATLAB. It provides an easy-to-use frontend, consisting of a GUI and an editor, which enables the user to create artificial lighting and daylight spectral simulations for arbitrary wavelengths without the need of additional software or code programming knowledge. Spectral fisheye images can easily be derived for any position and viewing direction. In combination with the complementary Lighting Toolbox for MATLAB and Octave, this allows for an in-depth spatial and spectral evaluation of the simulation results. LUMOS is therefore a suitable alternative for non-image forming effect research in cases where expensive measurement equipment or other software solutions are not affordable or available. Since the program runs within MATLAB, it can be operated on Windows, Linux and MacOS without restrictions. The source code and program are freely available via an open-source licence.
... The number of sky patches p is determined using the sky division method. Tregenza (1987) suggested dividing the sky vertically into eight bands subdivided by the azimuth. This results in 151 disk-shaped patches with widths close to 0.2 radians. ...
Accurate prediction of indoor daylight illuminance is crucial for daylight-based lighting controls. However, determining the illuminance using physics-based simulation tools requires significant amounts of information, e.g. grid of sensors, sky model, 3D geometry of a target building and surroundings, etc. In this study, the authors suggest a daylight illuminance estimation method with minimal data of two reference sensors and two prior measurements. It is shown that the daylight coefficient and sky luminance distribution can be substituted by the illuminance of the reference points and illuminance of two or more target points at past times. The method was validated on a large open space with north-facing skylight windows and showed an 11.9% mean absolute percentage error. Additionally, a reference point selection method is presented. The proposed method is practical for daylight-based lighting control applications.
... Calculation with Ladybug: the plugin for the analysis of weather data in Grasshopper uses the GenCumulativeSky algorithm [36]. This executable creates a discretised model of the sky dome made of 145 patches based on Tregenza subdivision [37] with specific solar radiation for each patch. The model is based on Perez expressions for sky luminance distribution [36,38]. ...
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One of the main targets of globally aimed strategies such as the UN-supported Race to Zero campaign or the European Green Deal is the decarbonisation of the building sector. The implementation of renewable energy sources in new urban structures, as well as the complex reconstruction of existing buildings, represents a key area of sustainable urban development. Supporting this approach, this paper introduces the solar-surface-area-to-volume ratio (Rsol) and the solar performance indicator (Psol), applicable for evaluation of the energy performance of basic building shapes at early design stages. The indicators are based on the preprocessors calculated using two different mathematical models—Robinson and Stone’s cumulative sky algorithm and Kittler and Mikler’s model—which are then compared and evaluated. Contrary to the commonly used surface-area-to-volume ratio, the proposed indicators estimate the potential for energy generation by active solar appliances integrated in the building envelope and allow optimisation of building shape in relation to potential energy losses and potential solar gains simultaneously. On the basis of the mathematical models, an online application optimising building shape to maximise sun-exposed surfaces has been developed. In connection with the solar-surface-area-to-volume ratio, it facilitates the quantitative evaluation of energy efficiency of various shapes by the wider professional public. The proposed indicators, verified in a case study presented, shall result in the increased sustainability of building sector by improving the utilisation of solar energy and overall energy performance of buildings.
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