The spatial statistics formalism applied to mapping electromagnetic radiation in urban areas

Abstract

Determining the electromagnetic radiation levels in urban areas is a complicated task. Various approaches have been taken, including numerical simulations using different models of propagation, sampling campaigns to measure field values with which to validate theoretical models, and the formalism of spatial statistics. In the work, we present here that this latter technique was used to construct maps of electric field and its associated uncertainty from experimental data. For this purpose, a field meter and a broadband probe sensitive in the 100-kHz-3-GHz frequency range were used to take 1,020 measurements around buildings and along the perimeter of the area. The distance between sampling points was 5 m. The results were stored in a geographic information system to facilitate data handling and analysis, in particular, the application of the formalism of spatial statistical to the analysis of the distribution of the field levels over the study area. The spatial structure was analyzed using the variographic technique, with the field levels at non-sampled points being interpolated by kriging. The results indicated that, in the urban area analyzed in the present work, the linear density of sampling points could be reduced to a distance which coincides with the length of the blocks of buildings without the statistical parameters varying significantly and with the field level maps being reproduced qualitatively and quantitatively.

Exposure assessment of mobile phone base station radiation in an outdoor environment using sequential surrogate modeling

“…LOLA, on the other hand, distributes the data points such that the density of the points is proportional to the local nonlinearity of the approximation function (in this case, the interpolation model), because dynamic regions are more difficult to approximate than linear regions. This dual strategy (combined using a weight function) results in a more efficient distribution of measurement locations compared to other traditional designs, such as uniform or random distributions used by Azpurua and Dos Ramos [2010], Joseph et al [2012a], and Paniagua et al [2012], for example. As an interpolation technique, we use cubic splines, which are smooth interpolating functions piecewise‐defined by third degree polynomials…”

“…Spectral measurements, on the other hand, involve band‐specific measurements and can be performed using two different types of measurement devices—spectrum analyzers (SAs) and personal exposure meters (exposimeters). Using these three types of devices, previous attempts have been aimed at geostatistical exposure prediction models (theoretical models), relying heavily on base station parameters, using exposimeter [Breckenkamp et al, 2008; Bürgi et al, 2008, 2010; Isselmou et al, 2008; Frei et al, 2009b] or SA measurements [Neitzke et al, 2007; Elliott et al, 2010; Joseph et al, 2012a] for optimization and validation, as well as measurement models interpolating exposimeter [Azpurua and Dos Ramos, 2010] or broadband measurements [Paniagua et al, 2012] at randomly or uniformly chosen locations.…”

Assessment of outdoor radiofrequency electromagnetic field exposure through hotspot localization using kriging-based sequential sampling

“…It takes into account the spatial structure of the interpolated variable (here, the electric-field strength), determines the best estimator of the variable (the error is minimized at all points), and it gives us information about the accuracy of the interpolation, by calculating an error estimate, called kriging variance (Matheron, 1963). Because of this, kriging is an often used interpolation technique in environmental research (e.g., Liu and Rossini, 1996;Paniagua et al, 2013;Sanders et al, 2012;Zirschky, 1985). The kriging variance can be used to quantify the model uncertainty, and to assist the sample search strategy in identifying potentially interesting regions in the study area based on a given condition.…”

“…As such, an efficient sampling scheme is constructed that ultimately results in a heat map of the outdoor RF-EMF exposure in a large area that features well-defined hotspots, representing important graphical information for risk communication. Using classical sampling methods (e.g., Joseph et al, 2012;Paniagua et al, 2013), it is not possible to identify and characterize hotspots except coincidentally. Validation…”

“…However, these approaches are heavily dependent on accurate data, e.g., base station parameters, building coordinates, building heights, etc., data which is seldom readily available. Measurementbased models, as found in Aerts et al (2013), Anglesio et al (2001), Azpurua and Dos Ramos (2010), Isselmou et al (2008), Paniagua et al (2013), on the other hand, encompass an accuracy that depends both on the number as well as the specific locations of the measurements. The importance of the latter can be seen from the fact that, in order to attain a similar accuracy, an area featuring a rapidly changing field distribution requires a denser sampling than an area of the same size featuring a more evenly field distribution.…”