# Variability of Diffuse Daylight Due to the Diversity of Cloud Arrays
## 1 Introduction  
Conventional energy resources such as fossil fuel are dwindling drastically as population grows, and, this goes hand in hand with constantly increasing needs for alternative energies. Therefore, it is not surprising that the importance of renewable energy supplies rises noticeably in all aspects of human life. In particular, solar energy is becoming an attractive candidate to meet future energy demands because of its abundance and global availability in the form of direct subbeams or diffuse daylight [1]. In addition to solar energy storing systems, direct and scattered sunlight are found to be very effective tools for energy saving in buildings [2]. Daylight delivery deeper into building interiors strongly depends on window orientation and sun path through the sky. Unshielded direct subbeams are known to be a major component of total luminous flux crossing the interface between outer and inner window interface. As the sunlight incidence angle approaches 90 degrees, the rapid crossover from direct to diffuse light dominance can be observed. Diffuse light is the only source of natural light that enters windows oriented sideward of the position of sun. Not surprisingly, the accurate modeling of sky luminance and illuminance is a key element in daylight research nowadays [3, 4].  
Angular distribution of diffuse light changes significantly with aerosol microphysics, especially the size of particles suspended in air [5]. Due to their large variability, the aerosol particles can intensify scattered light by several orders of magnitude depending on the angle contained by the direction to the sun and direction to a sky element. Therefore, empirical sky luminance models independent of aerosol properties usually fail to fulfil accuracy criteria imposed on advanced daylight predictions. Along with aerosols, clouds are the largest source of uncertainty in modeling the diffuse light since the clouds are of random shapes and distributed arbitrarily in the sky [6]. There are not many simple waysto treat the irregularity of a sky luminance pattern having its origin in cloud-reflected or cloud-masked light. Although the clouds can traverse sky or part of it, time-averaging over luminance distributions is not a reasonable approach because the mean luminance distribution obtained this way satisfies no one singular momentary sky state. Therefore, a use of average luminance distribution can result in unrealistic predictions of daylight availability for a few or many situations during a day. Averaged luminance distribution also suffers from loss of information on daily dynamics of luminance amplitudes. The latter can be important, e.g., for clouds accumulating in a sky quadrant opposite to the azimuthal position of the sun [7]. These clouds appear exceedingly bright compared to clear sky surrounding which luminance is reduced because of weak backscattering from realistically shaped aerosols.  
In this paper we show the range of diffuse illuminances on the horizontal surface and vertically oriented facades we can expect from broken cloud arrays in different situations. Contrasting to homogeneous luminance models, the real illuminance on the horizontal or a vertical plane exhibits a number of anomalous features under randomly arranged cloud fields. Numerical experiments are conducted to demonstrate illuminance amplitudes for a set of parameters, specifically cloud coverage, statistically averaged size of clouds, and cloud base altitude. The simulations are introduced in Section 2, while the results obtained are interpreted in Section 3.