عنوان مقاله [English]
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.
Materials & Methods
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.
Results & Discussion
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.
13. Anderson, M. C. (1964). Studies of the woodland light climate: I. The photographic computation of light conditions. The Journal of Ecology, 27-41.
14. Asawa, T., Hoyano, A., & Nakaohkubo, K. (2008). Thermal design tool for outdoor spaces based on heat balance simulation using a 3D-CAD system. Building and Environment, 43(12), 2112-2123. doi:10.1016/j.buildenv.2007.12.007
15. Bärring, L., Mattsson, J. O., & Lindqvist, S. (1985). Canyon geometry, street temperatures and urban heat island in Malmö, Sweden. International Journal of Climatology, 5(4), 433-444.
16. Bottyán, Z., & Unger, J. (2003). A multiple linear statistical model for estimating the mean maximum urban heat island. Theoretical and applied climatology, 75(3), 233-243.
17. Bradley, A., Thornes, J., & Chapman, L. (2001). A method to assess the variation of urban canyon geometry from sky view factor transects. Atmospheric Science Letters, 2(1‐4), 155-165.
18. Chapman, L., Thornes, J., & Bradley, A. (2001). Rapid determination of canyon geometry parameters for use in surface radiation budgets. Theoretical and applied climatology, 69(1), 81-89.
19. Chapman, L., Thornes, J. E., & Bradley, A. V. (2002). Sky-view factor approximation using GPS receivers. International Journal of Climatology, 22(5), 615-621. doi:10.1002/joc.649
20. Chapman, L., Thornes, J. E., Muller, J.-P., & McMuldroch, S. (2007). Potential applications of thermal fisheye imagery in urban environments. IEEE Geoscience and Remote Sensing Letters, 4(1), 56-59.
21. Chen, L., Ng, E., An, X., Ren, C., Lee, M., Wang, U., & He, Z. (2012). Sky view factor analysis of street canyons and its implications for daytime intra-urban air temperature differentials in high-rise, high-density urban areas of Hong Kong: a GIS-based simulation approach. International Journal of Climatology, 32(1), 121-136. doi:10.1002/joc.2243
22. Chun, B., & Guldmann, J. M. (2014). Spatial statistical analysis and simulation of the urban heat island in high-density central cities. Landscape and Urban Planning, 125, 76-88. doi:10.1016/j.landurbplan.2014.01.016
23. De Souza, L. C. L., & Da Silva, A. N. R. (2006). Applying GIS tools for analysing urban thermal environment. Paper presented at the PLEA 2006-23rd International Conference on Passive and Low Energy Architecture, Conference Proceedings.
24. Debbage, N. (2013). Sky-view factor estimation: A case study of Athens, Georgia. The Geographical Bulletin, 54(1), 49.
25. Drezner, T. D., & Shaker, R. R. (2010). A new technique for predicting the sky-view factor for urban heat island assessment. The Geographical Bulletin, 51(2), 85.
26. Eliasson, I. (1992). Infrared thermography and urban temperature patterns. International journal of remote sensing, 13(5), 869-879.
27. Esri. (2018a). Comparing models. Retrieved from http://desktop.arcgis.com/en/arcmap/latest/extensions/geostatistical-analyst/comparing-models.htm
28. Esri. (2018b). How Diffusion Interpolation With Barriers works. Retrieved from http://desktop.arcgis.com/en/arcmap/latest/extensions/geostatistical-analyst/how-diffusion-interpolation-with-barriers-works.htm
29. Esri. (2018c). How Kernel Interpolation With Barriers works. Retrieved from http://desktop.arcgis.com/en/arcmap/latest/extensions/geostatistical-analyst/how-kernel-interpolation-with-barriers-works.htm
30. Esri. (2018d). How Kriging works. Retrieved from http://desktop.arcgis.com/en/arcmap/10.3/tools/3d-analyst-toolbox/how-kriging-works.htm
31. Esri. (2018e). How local polynomial interpolation works. Retrieved from http://desktop.arcgis.com/en/arcmap/latest/extensions/geostatistical-analyst/how-local-polynomial-interpolation-works.htm
32. Esri. (2018f). How radial basis functions work. Retrieved from http://desktop.arcgis.com/en/arcmap/latest/extensions/geostatistical-analyst/how-radial-basis-functions-work.htm
33. Esri. (2018g). What is areal interpolation? Retrieved from http://desktop.arcgis.com/en/arcmap/latest/extensions/geostatistical-analyst/what-is-areal-interpolation.htm
34. Esri. (2018h). What is Empirical Bayesian kriging? Retrieved from http://desktop.arcgis.com/en/arcmap/latest/extensions/geostatistical-analyst/what-is-empirical-bayesian-kriging-.htm
35. Gál, T., Lindberg, F., & Unger, J. (2008). Computing continuous sky view factors using 3D urban raster and vector databases: comparison and application to urban climate. Theoretical and applied climatology, 95(1-2), 111-123. doi:10.1007/s00704-007-0362-9
36. Gál, T. M., Rzepa, M., Gromek, B., & Unger, J. (2007). Comparison between sky view factor values computed by two different methods in an urban environment. Acta Climatologica et Chorologica, 40, 17-26.
37. Grimmond, C., Potter, S., Zutter, H., & Souch, C. (2001). Rapid methods to estimate sky‐view factors applied to urban areas. International Journal of Climatology, 21(7), 903-913.
38. Hämmerle, M., Gál, T., Unger, J., & Matzarakis, A. (2011). Comparison of models calculating the sky view factor used for urban climate investigations. Theoretical and applied climatology, 105(3-4), 521-527. doi:10.1007/s00704-011-0402-3
39. Holmer, B. (1992). A simple operative method for determination of sky view factors in complex urban canyons from fisheye photographs. Meteorol. Z., NF, 1, 236-239.
40. Johnson, G. T., & Watson, I. D. (1984). The determination of view-factors in urban canyons. Journal of Climate and Applied Meteorology, 23(2), 329-335.
41. Jusuf, S. K., Ignatius, M., Wong, N. H., & Tan, E. (2017). STEVE Tool Plug-in for SketchUp: A User-Friendly Microclimatic Mapping Tool for Estate Development. In Sustainable Building and Built Environments to Mitigate Climate Change in the Tropics (pp. 113-130): Springer.
42. Krivoruchko, K. (2012). Empirical bayesian kriging. ArcUser Fall, 2012, 6-10.
43. Li, W., PUTRA, S., & Yang, P. (2004). GIS analysis for the climatic evaluation of 3D urban geometry. Paper presented at the Proceeding of seventh international seminar on GIS in developing countries (GISDECO).
44. Liang, J., Gong, J., Sun, J., Zhou, J., Li, W., Li, Y., . . . Shen, S. (2017). Automatic Sky View Factor Estimation from Street View Photographs—A Big Data Approach. Remote Sensing, 9(5). doi:10.3390/rs9050411
45. Lindberg, F., & Grimmond, C. S. B. (2010). Continuous sky view factor maps from high resolution urban digital elevation models. Climate Research, 42(3), 177-183. doi:10.3354/cr00882
46. Matuschek, O., & Matzarakis, A. (2011). A mapping tool for climatological applications. Meteorological Applications, 18(2), 230-237. doi:10.1002/met.233
47. Matzarakis, A., & Matuschek, O. (2011). Sky view factor as a parameter in applied climatology rapid estimation by the SkyHelios model. Meteorologische Zeitschrift, 20(1), 39-45. doi:10.1127/0941-2948/2011/0499
48. Matzarakis, A., Mayer, H., & Chmielewski, F.-M. (2010). Berichte des Meteorologischen Instituts der Albert-Ludwigs-Universität Freiburg. Retrieved from
49. Oke, T. R. (1981). Canyon geometry and the nocturnal urban heat island Comparison of scale model and field observations. JOURNAL OF CLIMATOLOGY, 1, 237-254.
50. Oke, T. R. (1988). Street design and urban canopy layer climate. Energy and Buildings, 11(1-3), 103-113. doi:10.1016/0378-7788(88)90026-6
51. Ratti, C. (2001). Urban analysis for environmental prediction. University of Cambridge,
52. Ratti, C., & Richens, P. (1999). Urban texture analysis with image processing techniques. In Computers in Building (pp. 49-64): Springer.
53. Ratti, C., & Richens, P. (2004). Raster Analysis of Urban Form. Environment and Planning B: Planning and Design, 31(2), 297-309. doi:10.1068/b2665
54. Souza, L. C. L., Rodrigues, D. S., & Mendes, J. F. (2003a). A 3D-gis extensionf for sky view factors assessment in urban environment.
55. Souza, L. C. L., Rodrigues, D. S., & Mendes, J. F. (2003b). Sky view factors estimation using a 3D-GIS extension.
56. Steyn, D. G. (1980). The calculation of view factors from fisheye‐lens photographs: Research note. Atmosphere-Ocean, 18(3), 254-258. doi:10.1080/07055900.1980.9649091
57. Svensson, M. K. (2004). Sky view factor analysis – implications for urban air temperature differences. Meteorological Applications, 11(3), 201-211. doi:10.1017/s1350482704001288
58. Unger, J. (2009). Connection between urban heat island and sky view factor approximated by a software tool on a 3D urban database. International Journal of Environment and Pollution, 36(1-3), 59-80.
59. Upmanis, H., & Chen, D. (1999). Influence of geographical factors and meteorological variables on nocturnal urban-park temperature differences—a case study of summer 1995 in Göteborg, Sweden. Climate Research, 13(2), 125-139.
60. Vieira, H., & Vasconcelos, J. (2003). Urban morphology characterisation to include in a GIS for climatic purposes in Lisbon. Discussion of two different methods. Paper presented at the Proc 5th Int Conf on Urban Climate.
61. Watson, I., & Johnson, G. (1987). Graphical estimation of sky view factors in urban environments. International Journal of Climatology, 7(2), 193-197.
62. Wong, N. H., Jusuf, S. K., & Tan, C. L. (2011). Integrated urban microclimate assessment method as a sustainable urban development and urban design tool. Landscape and Urban Planning, 100(4), 386-389. doi:10.1016/j.landurbplan.2011.02.012
63. Yamashita, S., Sekine, K., Shoda, M., Yamashita, K., & Hara, Y. (1986). On relationships between heat island and sky view factor in the cities of Tama River basin, Japan. Atmospheric Environment (1967), 20(4), 681-686.