Measuring heterogeneity in urban expansion via spatial entropy

The lack of efficiency in urban diffusion is a debated issue, important for biologists, urban specialists, planners and statisticians, both in developed and new developing countries. Many approaches have been considered to measure urban sprawl, i.e. chaotic urban expansion; such idea of chaos is here linked to the concept of entropy. Entropy, firstly introduced in information theory, rapidly became a standard tool in ecology, biology and geography to measure the degree of heterogeneity among observations; in these contexts, entropy measures should include spatial information. The aim of this paper is to employ a rigorous spatial entropy based approach to measure urban sprawl associated to the diffusion of metropolitan cities. In order to assess the performance of the considered measures, a comparative study is run over alternative urban scenarios; afterwards, measures are used to quantify the degree of disorder in the urban expansion of three cities in Europe. Results are easily interpretable and can be used both as an absolute measure of urban sprawl and for comparison over space and time.Comment: 23 pages, 7 figure

An Information Entropy-Based Sensitivity Analysis of Radar Sensing of Rough Surface

We apply Shannon entropy, an information content measure, in sensitivity analysis (SA), stemming from the fact that the essence of SA is to preserve the maximum information content of the parameters of interest that are inverted from the radar response. Then, the sensitivity to the observation configuration and surface parameters is subsequently analyzed. Attempts are also made to explore advantages, by maximizing the information content, of dual-polarization and multi-angle in improving the parameter retrieval from radar sensing of rough surface. Simulation results show that the entropy is a good indicator of the sensitivity of the radar response to the surface parameter, as it contains information on not only the probability distribution of the scattering coefficient but also on its deviation. By information entropy, richer details, to large extent, on the scattering behavior are offered through quantitatively predicting the scattering signal saturation, evaluating the effect of using multi-polarization and multi-angle observation configuration, and identifying non-significant variables. It is found that Shannon entropy, compared to Renyi entropy, appears to better represent the sensitivity with respect to monotonic variation and narrower parameter ranges. The proposed entropy-based SA method helps to deepen our understanding of the microwave scattering behavior in response to surface parameters