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The investigation of mashhad's heat island by using satellite images and fractal theory (box counting method).


Heat island is one of the phenomena that affects human beings' life environment in urban areas on a large scale. The Heat islands form when an extra percentage of surface natural covering is wiped out and replaced with buildings, roads and other urban constructions. This problem results in the trammel of the ripe solar radiation into urban structures during the day and its reflection at night. Thus the natural process of earth surface getting cold during the night happens more slowly and consequently, the air temperature of cities will be naturally higher than the air temperature of suburb regions (Oke, 1973). This temperature difference is sometimes up to 5 to 6 degree Celsius; and even in some big cities the difference of 6 to 8 degree Celsius in clear and calm nights, has been reported (Barry and Chorley, 1987). As a result, the intensity of heat island depends on the meteorological systems, which contains the maximum amount in calm (without wind) and clear nights (Yague et al 1991, Klysik & Fortuniak 1999, Montaves et al 2000). About one century ago, Haward coined the term heat island for the first time in 1833 (Solecke, 2004). Afterwards, several researches were done in great and industrial cities the results of which reveal that urbanization causes considerable changes on meteorological parameters and characteristics of earth surface, and consequently, more variations in the situation of local weather and climate (Atwater 1972 & 1974, Changnon 1981, Cotton & Pielke 1995, Baik & Chun 1997, Tumanov et al 1999) .According to Oke, the influence of heat island on temperature is more than other meteorological parameters (Oke, 1982). He also showed that low puff and the existence of an anticyclone in a clear sky, may prepare the appropriate conditions for the formation of a partly hard heat island. The researches done in London showed that since 1931 to 1960 the annual average of air temperature in this city was 11 degree Celsius; while in the suburb and in the village areas of environs it was 10.3 and 9.6 degree Celsius respectively. This temperature difference proves the occurrence of a heat island in London (Barry and Chorley, 1987). Also, another study was performed in Beijing, China on the heat island. In this project, the amounts of earth surface radiation temperature (SRT) were extracted from a TM image of Landsat satellite (Xiao, 2002). The analysis of the air temperature difference between Saint Juan, a coast city in Puerto Rico, and its environs proved the existence of a heat island and indicated that its temperature has been increasing at the rate of 0.06 degree Celsius a year since forty years ago; and that totally in forty years, it has increased about 2.4 C (Velazquez, 2006). Mousavi-Bygi and his colleagues (Mousavi-Bygi et al, 2010) investigated Tehran's heat island by using the surface ozone and temperature data. They showed that the amount of ozone and temperature has been increased in Tehran. Xiao-Ling and his team used the TM and ETM+ images of Landsat and proved an urban heat island in one of the metropolises of China during 1990-2000 (Xiao-Ling et al, 2006). Also in the US, this phenomenon was investigated by using ASTER images and results showed that urban heat island is more severe at night than during the day (Hartz et al, 2006).The findings of researchers done in Arizona and Tucson in America showed that the local winds of low levels of atmosphere diminish the effects of heat island remarkably and that there will be no possibility of heat island formation, if there is a downfall of cold air from neighbor vales (Comrie, 2000). The results of other researches done in Seoul also revealed that the maximum amount of heat island occurs in autumn and winter and the minimum amount of it occurs in spring and summer (Kim & Baik, 2001). In Singapore also, a research was done on the effects of plant covering and landscape in reducing the probability of heat island formation (Wong, 2005). Because of its important effects on environment and health, urban heat island was evaluated in Mashhad, as a metropolis in Iran, by using remote sensing and fractal theory. Surface radiant emittance, as recorded by thermal infrared sensors, includes both topographically and non-topographically induced high frequency variations such as roads and edges caused by different spectral characteristics of different neighboring land covers (Lam, 1990). The spatial surfaces generated from thermal infrared image data therefore have a fractal characteristic that mixes topographic and non-topographic frequencies. The use of fractals for analyzing thermal infrared images will improve our understanding of the thermal behavior of different land-cover types and the effects of landscape pattern on thermal environmental processes. Moreover, because the remote sensing analysis of the urban heat islands often involve multiple sensors, it will be critical to know if fractal dimension is predictable with changes in spatial and spectral resolutions. Evaluating urban heat island by applying the TM and ETM+ images, all of the investigations in the word showed that the fractal dimension in the urban area is more than in the suburb (De Cola, 1989, Lam, 1990, Emerson et al, 1999, Qiu et al, 1999, Weng, ,2003).

Materials and methods

Study Area

Mashhad is located at latitude 36 17' 45"-N and longitude 59 36' 43"-E and with a population of 2410800 is one of the metropolises of Iran. Also because of Holy Shrine, many pilgrims come to Mashhad every year, so the problems can be more critical in this big city. An extra percentage of surface natural covering is wiped out and replaced with urban constructions and many of landscapes have changed to residential area to place people in.

Investigation of the temperature trend

In this study we used the maximum and minimum temperature of Mashhad during 1992-2002 to probe the temperature trend and occurrence of urban heat island in Mashhad during these years. Therefore we plotted the monthly average temperature in 1992-2002 and the annually average temperature in synoptic hours (Figure 2.a, b and c). But because there isn't enough data for investigating and comparing the temperature trend in the city and suburb, so we applied the satellite images and Fractal theory. Since the thermal band of Landsat (Band 6) can show the surface radiant well and urban heat island is a result of surface radiant temperature, so we can show increasing temperature by using these images. Urban development increased the spatial variability of radiant temperatures, resulting in higher fractal dimension values. So calculating the fractal dimension of the satellite images as the indicator of spatial variability can help the researchers to confirm the occurrence of urban heat island.

Calculation of surface radiant temperatures

The data used in this study were the Landsat Thematic Mapper (TM) and Enhanced Thematic Mapper Plus (ETM+) images, dated on 25 July 1992 and 6 August 2002, respectively. Each Landsat image was rectified to a common UTM coordinate system based on 1:50,000-scale topographic maps. Although the impact of the diurnal heating cycle on the urban heat islands will be an interesting issue to address, there has been no attempt to include it here, because TM and ETM+ does not provide day and night infrared images at the same day. By using a quadratic model, we can convert the digital number (DN) into radiant temperatures for a TM image as follows (Malaret et al., 1985):

T (k) = 209.831 + 0.834DN--[0.00133DN.sup.2]

For an ETM+ image, thermal band image data calibration is performed in a two-step process as proposed by the Landsat Project Science Office (2002): (a) conversion of the digital number (DN) values of band 6 into the spectral radiance (L) ([Wm.sup.-2] [sr.sup.-1] [lm.sup.-1]) using the following equation: L = 0.0370588DN + 3.2

and then (b) the conversion of the spectral radiance (L) to at-sensor brightness temperature (T(k)) in Kelvin. The conversion formula is given by:

T (k) = [K.sub.2]/ln([K.sub.1]/L + 1)

where T(k) is the at-sensor brightness temperature in Kelvin, K2 is the calibration constant (1282.71 K) and K1 is the calibration constant (666.09 [Wm.sup.-2] [sr.sup.-1] [lm.sup.-1]).

However, the temperature values obtained above are referenced to a black body. Therefore, the corrections for emissivity ([epsilon]) became necessary according to the nature of land cover. Vegetated areas were given a value of 0.95 and non-vegetated areas 0.92 (Nichol, 1994). The emissivity corrected surface temperatures were computed as follows (Artis and Carnhan, 1982):

[T.sub.s] = T9k)/1 + [lambda]T(k)/[rho] ln [epsilon]

where [lambda] is the wavelength of emitted radiance for which the peak responses and the average of the limiting wavelengths, [lambda] = 11.5 um will be used(Markham and Barker, 1985). In this equation [rho] can be derived by the following formula:

[rho = hc/[sigma]

where [sigma] is the Stefan Boltzmann's constant (5.67 x [10.sup.-8] W [m.sup.-2] [K.sup.-4),], h is Planck's constant (6.626 x [10.sup.34] J sec), and c is the velocity of light (2.998 x [10.sup.8] m/sec). So the amount of p will be 1.438 x [10.sup.-2] mK. Vegetated and non-vegetated areas were determined by the NDVI image for each year. All the mentioned equations were implemented by ERDAS and ARC GIS. Figure 3 shows the temperature maps.

Derivation of land use

Figure 4, which is derived based on NDVI, shows the vegetated and non-vegetated areas. So for deriving the temperature map, we applied it. Also we need the land use to investigate the relationship between urban heat island and land use. The categories of land use include urban or built-up land, barren land, cropland, horticulture farms, pasture, forest and water (Anderson et al, 1976). From these maps, it is clear that there have been considerable changes in land use in Mashhad during the 10-year period.

Estimation of fractal dimension

Fractal geometry was introduced and popularized by Mandelbrot (1977) to model natural shapes (e.g., coastlines and terrain) as well as other complex forms that traditional Euclidean geometry fails to analyze. Fractals have two basic characteristics suitable for modeling the topography and other spatial surfaces in the Earth's surface: self-similarity and randomness. Self-similarity refers to the well-known observation that the Earth's morphology appears similar across a range of scales. The concept of self-similarity also contains randomness, because the resemblance of the Earth's morphology at different scales is not exact but statistical (Malinverno, 1995). A fractal construction that includes randomness is termed a self-affine fractal. Self-affine fractals, such as fractional Brownian motion, requires rescaling by different coordinates for an enlargement to look like the original, and have been used to model the topography of the Earth's surface (Mandelbrot, 1983). Since the remote sensing imagery is considered as a kind of spatial surface, so the complexity of it can be described by fractal models especially by self-affine fractals (Lam, 1990). The fractal dimension of the spatial surfaces and profiles of remotely sensed data may be estimated using one of four main methods: the box-counting method, the spectral method, the divider method and the triangular prism method. In this study we use the box counting method. The box-counting method is implemented by laying a regular grid of boxes of characteristic size over the profile and counting the number of boxes intersected by the profile. The process is repeated for different sizes of box, and the number of boxes filled is plotted against the total number of boxes in the grid in a log-log form. If linear, the slope of this curve is related to the fractal dimension.


The algorithm used in this study was originally developed by Goodchild (1980) and Shelberg et al. (1983), and elaborated in Lam (1990) and Jaggi et al. (1993). This algorithm measures the fractal dimension of isarithm lines characterizing a spatial surface, and averages the dimension values of all lines as the surface's final fractal dimension. The isarithm lines of a remotely sensed image are generated by dividing the range of the pixel values of the image into equally spaced intervals. The length of each isarithm, as represented by the number of edges, is then measured at various step sizes. The logarithm of the number of edges is regressed against the logarithm of the step sizes. The slope of the regression is obtained using a best-fit linear model, and thus a dimension value for the isarithm.

Results and discussion

Figure 2 shows the monthly average temperature (a, b) in 1992-2002 and the annually average temperature in synoptic hours (c). As the figure shows, air temperature in this city has been increasing during this 10-year period generally and this increasing is recognized in all months and all hours. So we can conclude that the urban heat island has happened in Mashhad.


Figure 3 shows the spatial distribution of the surface radiant temperatures on July 25th 1992 and on august 6th 2002. It is clear from the map that all the urban or built-up areas have a relatively high temperature. Also it is clear that the surface radiant temperatures have increased in 2002 than 1992. Although the temperature in July is more than in August generally, but increasing of the temperature has been so much that the temperature in August 2002 is more than in July 1992. In this figure we have also shown three profiles including north-south, east-west and northwest--southeast. The temperature trend and urban development has been shown in these three profiles.



Because of being near the desert and not having the dense vegetation, Mashhad experiences a very high temperature generally. As figure 3 shows, the east south areas of Mashhad has much more temperature even than built-up areas. This area is usually barren or has much dispersed vegetation. Figure 4 shows the vegetated and non-vegetated areas in Mashhad. Figure 3 and 4 shows that there is a relationship between the surface radiant temperature and vegetation. Figure 4 also shows that the vegetation has diminished severely in 2002 than 1992.


The resultant land-use maps for 1992 and 2002 are displayed in figure 5. From these maps, it is clear that there have been considerable changes in land use in Mashhad during the 10-year period. Some horticulture areas in the city have been removed and replaced by buildings and constructions (see Malek Abad garden in figure 6 that has been shown by an arrow). Also in the north of the city some of the landscapes have altered into built-up area. As figure 3 and 4 show, vegetation in these areas has diminished and therefore temperature has increased. In the intersection of three profiles, Temperature is about 36.4 in 1992 image and 42.8 in 2002 image. This point is around the Holy Shrine and so is very crowded. Therefore in this point and the areas around it temperature is much more than other areas. Average temperature in these areas is 38.4 in 1992 image and 44.5 in 2002 image. In Malek Abad garden, the temperature is 26.6 in 1992 image and 29.7 in 2002 image. These results show that the increasing of temperature in built-up areas (around Holy Shrine) is more than in horticulture areas (Malek Abad garden) and this means that urban heat island has happened in Mashhad.

Figure 6 shows the magnified image of Mashhad to display the more details of temperature variability and land use. It can confirm the above-mentioned point.


Land use maps show that non-irrigated croplands have diminished in 2002 than 1992 as rain has decreased. But it should be mentioned that in August 2002 lots of non-irrigated crops have been harvested. Like barren areas, pastures around Mashhad experience high temperatures.

The calculated values of fractal dimension confirm this observation. Table 1 shows the fractal dimension and average temperature of three profiles on magnified maps of temperature (figure 6, b and d).

The relatively low values of fractal dimension suggest that the texture is less spatially complex. It means that the spectral responses to the thermal band along the line tend not to vary drastically. In urban areas because of unsteady vegetation and roughness variability, the fractal dimension has a high value. In northwest--southeast profile where urban or built-up cover has occupied the majority of the surface, the fractal dimension in both images is upper than other profiles (table 1). In spite of high fractal dimension, the average temperature in this profile is less than other profiles, because this profile has occupied more horticulture and cropland area than other profiles. But the average temperature of urban areas in northwest--southeast profile is higher than north-south and east-west profiles. This result is true for both year 1992 and 2002. Because in east-west profile, urban area has developed more severely since 1992 to 2002, the fractal dimension has increased more than other profiles.


The utility of Landsat TM infrared data to detect urban heat islands in Mashhad proved to be effective. The distribution of the urban heat island was closely associated with industrial and residential land uses. Changes in fractal dimension were attributed to the topographic variation and the spatial arrangement and areal extent of different land cover types. Urban development increased the spatial variability of radiant temperatures, resulting in higher fractal dimension values. The thermal surfaces have become more spatially uneven and the textures more complex. So we can conclude that urban development results in increasing of spatial variability and the fractal dimension.


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Ameneh Mianabadi (1) * and Alireza Farid (2)

(1) M.Sc. of Agrometeorology (2) Assistant Professor, Water Engineering Department, Ferdowsi University of Mashhad-Iran

* Corresponding Author
Table 1: fractal dimension and average temperature of three profiles
on magnified maps.

Year profile Fractal Avg. temperature Avg. temperature of
 D. of whole profile built-up

1992 N-S 1.23 37.4 36.4
 E-W 1.20 36.1 36.1
 NW-SE 1.41 32.9 37.1
2002 N-S 1.27 43.5 36.9
 E-W 1.35 42.3 36.7
 NW-SE 1.49 39.8 41.1
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Author:Mianabadi, Ameneh; Farid, Alireza
Publication:International Journal of Applied Environmental Sciences
Date:May 1, 2011
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