As a powerful tool for assessing cities development, the emergy synthesis considers the energy quality concept, which allows it to quantify all the effort provided by nature in providing resources, however, it usually demands a huge amount of data and still lacks a complete and updated database for long-term studies. Cities seem to develop according to fractals, building up parts that resemble the whole, which is also relevant in emergy theory and observable through night-time lights from cities that are used to investigate how energy use distributes as cities change. This work proposes an alternative method for estimating the fractal dimension and non-renewable empower density (NRED) of cities from satellite night-time images and assess the relationship between them. Nine cities in Brazil, selected through a cluster analysis, were considered as a case study. Results show a strong positive correlation (0.94 for Pearson index) between fractals and NRED, which can be of help in estimating each other for further studies. The method proposed is time and cost effective when compared to previously used methods based on red/blue/green (RBG) satellite images, representing a potential alternative for assessing urban expansion in spatiotemporal models and assessing cities limits to growth.

作为评估城市发展的有力工具，能效综合考虑了能源质量概念，可以量化自然界在提供资源方面的所有努力，但是，它通常需要大量数据，但仍缺乏完整和更新的信息长期研究的数据库。城市似乎是按照分形发展的，组成了类似于整体的部分，这在能值理论中也很重要，并且可以通过夜间夜间照明灯从城市中观察到，用来研究能源使用量如何随着城市变化而分布。这项工作提出了一种替代方法，用于从卫星夜间图像估计城市的分形维数和不可更新的授权密度（NRED），并评估它们之间的关系。通过聚类分析选择了巴西的9个城市，被认为是一个案例研究。结果表明，分形与NRED之间存在很强的正相关（Pearson指数为0.94），这有助于相互评估以进行进一步的研究。与以前使用的基于红/蓝/绿（RBG）卫星图像的方法相比，提出的方法既省时又节省成本，是在时空模型中评估城市扩展和评估城市增长极限的一种潜在选择。