Probability Density Distribution Model For Nighttime Light Composite Data

Nighttime light (NTL) remote sensing has close relationship with human activities. It captures lights at night, such as artificial lights, fires and moonlights. So far nighttime light imageries has been proven to be good indicators in various aspects related to human activities including estimation of social and economic indicators, estimation of ecology and environment, and analysis of urbanization, wars and natural disasters. However, few studies have focused on the fundamental characteristics, interpretation of formation mechanism and explanation of exceptions existing in present studies on nighttime lights.To bridge the gap, this paper focuses on the introduction of the probability density function (PDF) and the analysis of its basic properties, application and the formation mechanism using the NTL composite data recorded from Visible Infrared Imaging Radiometer Suite (VIIRS) of Suomi National Polar-orbiting Partnership (NPP) and Operational Linescan System (OLS) of Defense Meteorological Satellite Program (DMSP).The main topic and results of this paper are as follows:1) This paper systematically studied the NTL PDF distribution model. Firstly, the definition of PDF distribution and the estimation of the empirical PDF distribution of NTL data are introduced. Secondly, it is found that the overall NTL PDF distribution is the mixture of two components including urban and non-urban PDF distributions. Meanwhile, for the PDF distribution of urban and non-urban components, their tails strictly follow power law. In addition, in this paper, NTL PDF distribution for urban and nonurban areas are proven to follow Double Pareto Lognormal (DPLN) distribution. Parameters of the mixture DPLN model for overall NTL distribution fitted by combining the maximum likelihood method and the interior point method.2) Based on the mixture of DPLN model, this paper presents a new thresholding method using the trust region algorithm to extract urban areas. To validate the method, 39 cities of USA are selected as case study areas. Results show that it is an effective urban extraction method. Firstly, it is easy to be implemented and requires no assistant data and parameter training. Also, compared to existing methods, it performs better with greater accuracy. Lastly, this method can be effectively applied to both NPP/VIIRS NTL data and the calibrated DMSP/OLS NTL data. For the well-known special study area of Nile River Delta, from the perspective of mixture of DPLN distribution, this paper studied and explained the abnormal phenomenon of its NTL distribution and deduced the principle of Head-Tail Break through mixture of DPLN distribution.