Estimation of sky view factor (SVF)an empirical comparison of interpolation models

Obtaining reliable environmental values in vast geographic areas is usually costly and difficult; therefore, the ability to predict unknown values or in other words, the use of better interpolation methods is very important. Interpolation methods utilize a set of different mathematical and statistical models to predict the unknown values. The similarity of the unknown points to the nearest known points or the principle of the nearest neighbor is the basis of interpolation methods, and how this principle is used depends on the selected model. In a general classification, interpolation methods are divided into two large classes. The first method is deterministic, in which interpolation is carried out based on determining the level of sampled points and also based on the similarities such as Inverse Distance Weighting (IDW) method or Radial Basis Function (RBFs). In the second method, interpolation is probabilistic – geostatistical, that is done based on the statistical properties of the sampled points. On the other hand, due to the growing increase in the problems of urbanization and urban heat islands, current cities need to have a detailed planning for future developments and preserving the quality of urban environment. Also, the geometry of urban valleys, which is defined by changing the height, length and distance of buildings, has a significant impact on the energy exchange and thus, the temperature of urban areas. But, this temperature, in turn, depends on a number of geographical - geometric factors (such as SVF) and meteorological variables. The Sky View Factor (SVF), as one of the usual indicators of describing urban geometry that refers to the amount of sky observable from a point on the Earth, has become one of the most important predictors of UHI due to its applicability in the urban climate, its contribution to the spatial data, and the existence of available techniques. In the climatic studies, the SVF is also considered as an important geometric parameter due to its correlation with the local temperature performance and its potential importance in the urban design process.Although urban Climatologists know this indicator well, it is not that much known among the urban designers and planners. This issue has not progressed much in Iran and there are no reliable sources about it. Despite the fact that different methods and models have been introduced for interpolation of Point data, no specific method has been proposed for estimating this index. Hence, this study has empirically compared the interpolation models with an emphasis on the Empirical Bayesian Kriging (EBK). This comparison is important since EBK has automated the most difficult aspects of the construction of a kriging model. This is while in other Kriging methods, the parameters are adjusted manually to obtain accurate results. EBK automatically simulates and calculates these parameters through a setup process. In classical kriging, it is also assumed that the estimated semivariogram is a true semivariogram of the observed data. This means that the data are generated from Gaussian distribution with the correlation structure defined by the estimated semivariogram. This is a very strong assumption, and it rarely holds true in practice. Accordingly, measures should be taken to make the statistical model more realistic. 

 The present study is an applied research in terms of its objective and it is quantitative in terms of the data analysis method. The study area is district 6 of Shiraz Municipality (496 hectares). Due to the multiplicity of interpolation methods and techniques as well as kernel functions and model fit functions, about 138 interpolation scenarios arewereimplemented. Also, four indices of Root-Mean-Square (RMS), Mean Standardized (MS), Root-Mean-Square Standardized (RMSS) and Average Standard Error (ASE) have been used for evaluating the models. The input data (sample) contains 6157 points, measured at intervals of 30 m distances in the study area. These points are werecreated based on the SVF calculation software method and using the GIS base model in ArcGIS10.6.  

Out of 138 scenarios, seven scenarios with the lowest RMS values arewereseparately examined in detail taking into account three other indicators. Another variable called “Neighborhood type” iswas added to the surveys in two standard and smooth modes. The results show that simple kriging and EBK have better results than the other models. Also, among the simple Kriging fitted models, the RQ model shows better results than other fitting models.  

Based on the RMS index, EBK is one of the best reliable automatic interpolation models (ranked second) for estimating the SVF. In general, based on RMS, MS, RMSS, it is the best automatic interpolation model for estimating SVF.