A Satellite-Based Sky Luminance Model for the Tropics

Serm Janjai

doi:10.1155/2013/260319

Abstract

This paper presents a sky luminance model for the tropics. The model is mathematically expressed as a multiplication of two functions. These areφ, which is a function of the zenith angle of a sky element and solar zenith angle, andf, which is a function of the angle between the sky element and the sun. To obtain the analytical forms of these functions, the sky luminance data collected at Nakhon Pathom (13.82°N, 100.04°E), Thailand, during a four-year period were analyzed. Additionally, satellite-derived cloud index at the position of the sky luminance measurements during the same period was estimated. Based on values of the cloud index, the skies were classified into 10 types, from clear to overcast skies. By using appropriate grouping and mathematical operation of the sky luminance data, the values of the two functions were obtained and then fitted with empirical equations. The multiplication of these equations gives the final form of the sky luminance model. To validate the model, it was used to calculate the relative sky luminance at other three sites in the tropics. It was found that values of relative sky luminance calculated from the model and those obtained from the measurements were in reasonable agreement.

Highlights

A utilization of daylight to illuminate building interior helps to save electricity for lighting [1]
Information on sky luminance should be obtained from a dense network of sky scanners, but due to costs, only a few instruments are routinely deployed in most parts of the world, and limited works on sky luminance measurements have been reported [5,6,7,8]
As it is difficult to find a function to represent mathematically the absolute sky luminance, most investigators [10, 18, 19] preferred to formulate a model for a relative sky luminance (Lrel) which is defined as a ratio of the absolute sky luminance (L) to the zenith luminance (Lz)

Summary

Introduction

A utilization of daylight to illuminate building interior helps to save electricity for lighting [1]. To avoid the use of solar radiation and other meteorological data and the problem of subjectivity to identify sky types, we proposed a novel method to identify sky conditions by using satellite-derived cloud index, and a new formula for estimating sky luminance was established using this identification method. To ensure the generality of the model for the tropics, sky luminance independent data obtained from other 3 stations situated in the tropical environment were used to validate the model. The distance between these stations varies in the range of 600– 1,500 km

Measurements and Data Processing

Modeling

Validation of the Model

Conclusion