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Methodology solar buildings and cities should be designed based on urban design, building form/geometry, and solar energy principles. Also, studies have shown the importance of geographic and climatic factors in solar energy potential and absorption. The transmission of solar energy depends on environmental factors (Iqbal, 1983). Accordingly, environmental (natural) factors should also be analyzed to optimize environmental (man-made) elements during the design, regeneration, and restoration process. The aim of this paper is the evaluation of the solar eﬀects in buildings, especially in Tabriz city in northwest Iran.

The paper concentrated on the solar conditions of the blue mosque (bm) an important building of Islamic Azerbaijani architecture in Iran. Qualitative, qualitative, and statistical methods were used to analyze the bm. Tabriz city has high-density features that were selected as case studies to estimate their solar radiation and climatic and geographic conditions. The solar energy re potential of Tabriz was modeled statistically and graphically using spss, ms excel, and ladybug for grasshopper.

Climatic and geographic analysis of Tabriz city.

Tabriz is located in the Northwest part of Iran (Fig. 4). The city is located 38°5’ north of the equator and 46°16′ east of Greenwich. Tabriz city has a great need for domesticating solar energy because of its climatic situation and geographical position. Its climate is classified as BSk by Köppen and Geiger (Kottek, 2006).), with harsh winters and hot dry summers. Fig. 4. Location of Case Study Averagely, the city`s altitude is 1361 meters above sea level. Humidity is low in both summer and winter. The geographical location of stations is presented in table 3.

Dew point and dry bulb temperatures, and relative humidity of the city have been shown using Lady Bug in Rhino software in Fig.5 respectively. Table 3. The geographical location of stations Latitude (φ) (deg.) Altitude (m) Longitude (degree) 38°5′ (N) 1361 m 46°16′ The used parameters inputted in the analyses have been taken from the Energy Plus database. The average annual rainfall is 323 mm. The average monthly temperature is 11.6 °C in a cold climate. The diﬀerences between the warmest and coldest months are 41 °C, with at least four months below -3°C. Fig.5 a-c.

The land cover is important in the rate of solar energy reﬂection which requires a detailed analysis of land cover types and their portions impacting urban heat islands (Ouria & Sevinc, 2017; Xu, Wang, & Xiao, 2000). Accordingly, the distribution of land cover/ use in Tabriz City was analyzed. Then, the albedo constant in Tabriz City was calculated based on the proportion of diﬀerent materials colors, proportion, and GIS data used in the urban land cover (Fig. 6.). Fig.6. Land use/cover in the state of Tabriz after 2016. Analyzing land cover type is crucial, especially in regions with limited physical extents (Qingqing et al., 2012; Ouria & Sevinc, 2017). To analyze the solar energy in an area, its land cover and type of use are necessary parameters because they have diﬀerent reactions to solar radiation. Fig. 7 presented the distribution of the land cover in Tabriz. According to the land cover data given in (Figs. 6–8), around 9869 ha of the city is allocated for the urban areas, which includes 56% of the total areas. 600 ha for the forested area, which presents just 3% of the total covered area. Bare ground covers 785 ha or 5%, and Open Land (Light Soil and Grass) 880.41 ha, which presents 9%. Open Land (Military and airport facilities) shows 10% (1586 ha) of the total covered area. Fig.7. Diﬀerent areas of land use/cover in the state of Tabriz after 2016 Fig.8. The land cover portions of Tabriz after 2016 Albedo/reﬂectivity of diﬀerent surfaces, depends on two important parameters including the surface areas proportion and surface reﬂection ratios (Ouria & Sevinc, 2017). The rate of land areas was computed using GIS data for Tabriz City. So, table 4, presented the reﬂectivity of diﬀerent surfaces (Oke, 1973; Ahrens, 2006). It should be highlighted that the albedo coeﬃcient (0.23) is calculated for the urban scale of the Tabriz region by evaluating the area of the cover types and their special coeﬃcients. Accordingly, the micro-scale of environmental factors for each building should be focused on. The albedo rates in diﬀerent districts of the city are diﬀerent. Subsequently, the percentage of each type of cover has been given in Table 1. Although the reﬂectivity rate changes from 0.2 to 0.5, the lower rate of albedo in Tabriz (0.23) does help citizens feel that the urban spaces are more comfortable. Table 4. Average Albedo Value of Land Covers in Tabriz City. Cover Types Covered Area (ha) Covered Area(%) Albedo Coeﬃcient Albedo Portion Urban (Stone and Metals with medium Density) 9869 56% 0.18 10.08% Farmlands 3070.77 17% 0.28 4.76% Open Land (Military and airport facilities) 1836.57 10% 0.25 2.5% Open Land (Light Soil and Grass) 1586.862 9% 0.44 3.96% Bare Ground (light and dry) 786.4314 5% 0.24 1.2% Scrub forest 600.46 3% 0.2 0.06% Average Constant for Tabriz 17747.1939 100% – 22.56% Monthly and Hourly Solar Radiation of Horizontal Surfaces in Tabriz City Regression model studied to calculate the amount of radiation and coefficients of each models by SPSS software after quality control data contained in Tabriz station. There are some independent parameters such as; mean temperature, humidity, cloudiness, and sunshine, and their correlation are shown in table 5. Table 5: The correlation of climatic variables on the amount of solar radiation Climatic Elements Mean Temperature Relative Humidity Cloudiness Sunshine Radiation Radiation Pearson Correlation 0.88** -0.82** -0.68** 0.92** 1 0.00 0.00 0.00 0.00 Sig. (2-tailed) N 70 70 70 70 **. Correlation is significant at the 0.01 level (2-tailed). According to the data in table 5, sunshine has a maximum correlation with solar radiation. By the use of independent parameters of table 5 implement, the (Enter Method) regression model of solar radiation has been used according to the climatic parameters of Tabriz. The coefficients and amount of entered variables in the model are presented in table 6. A summary of indicators regression by entering the Model is presented in table 7. Table 6. Regression Coefficients of Variables in Model of entering Variable Unstandardized Coefficients Standardized Coefficients Statistics T Significance Level B Std. Error Beta Constant Factor Model -6906.58 1023.49 – -6.74 0.00 Mean Temperature 250.53 208.76 1.5 1.2 0.23 Relative Humidity -1.36 8.11 -0.01 -0.16 0.86 Cloudiness 701.97 57.68 0.68 12.17 0.87 Sunshine 930.99 55.52 1.5 16.77 0.00 Table 7. Summary of regression indicators by entering Model Model R R Square Adjusted R Square Std. The error of the Estimate Durbin-Watson 1 0.98 0.96 0.95 335.3 1.8 Linear relationship between the variables is asserted by regression analysis of variance. Because The significance level is zero which is less than alpha levels of 0.01 and 0.05 (Table. 8). Table 8. Regression Analysis of Variance Model Sum of Squares df Mean Square F Sig. Regression 182388698.9 4 30398116.49 270.37 0.00 Residual 7307831.39 66 112428.17 Total 189696530.33 70

The monthly average global radiation on a horizontal surface measured by the Tabriz station and the estimated model are presented as follows; Fig.9. Comparing the Measured and Modeled Monthly Mean Solar Radiation of Horizontal Surfaces in Tabriz City The components of the hourly solar radiation, such as diﬀuse radiation, global solar radiation and direct radiation in Tabriz, has been generated by the Ladybug for Grasshopper Program. In this model, the rate of each component is calculated according to the solar azimuth annually as shown in Fig. 10. For example, in April, the minimum rate of direct normal radiation by 140 wh/m2 is noticeable, while it reaches above 340 wh/m2 in Jun after 09:00 am. Regarding global horizontal radiation, there is a noticeable amount of radiation between 09:00 am and 02:00 pm in a range from Jun to October. Fig.10. Hourly Horizontal Radiation SOLAR RADIATION COMPONENTS AT GROUND LEVEL Table 9 shows the monthly sunny hours, clearness index, and solar times of Tabriz City according to equations 22 and 23. Potentially, Tabriz City has 4369 sunlight hours, but 30% of this amount is wasted during hazy, cloudy, and foggy days. There are only 3047 sunny hours. Table 9. Monthly Sunny Hours, Solar Time, and Clearness Index of Tabriz City. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Sb (hrs) 5.4 5.9 6.7 7.8 10.3 12.7 12.7 11.6 10.6 4.2 6.4 5.9 Sp (hrs) 9.8 10.5 11.7 13 13.75 14.2 14.11 13.5 12.5 11 10.1 9.5 0.55 0.56 0.57 0.6 0.74 0.89 0.9 0.9 0.84 0.38 0.63 0.62 According to equation 8, the solar altitude average is 52° on March 21 at solar noon, while it decreases to 28° on December 21 and rises to 78° on June 21. Fig. 11. shows altitude angles at solar noon on Tabriz (latitude 38) in monthly average degree. Fig. 11. Altitude angles at solar noon According to equation 9, the solar azimuth angle of Tabriz City is presented in Fig. 12 using Microsoft Excel. The values are calculated for the monthly mean.

The solar azimuth angle at sunrise is 90° on March 21 at 6:00, while it decreases to 60° on June 21 and rises to 120° on December 2. Fig. 12. Azimuth Angle of Tabriz City The annual solar radiation components, such as diﬀuse radiation, global solar radiation, and direct radiation in Tabriz, were again generated by the Ladybug for Grasshopper Program. In this model, Sothern facades (a range from 91 to 179 degrees) are exposed to the maximum rate of energy by 400 kWh/m2, 500 kW/m2, and 900 kW/m2 for direct, defused and total radiation respectively, while Northern facades (a range from 181 to 89 degree) are exposed in the minimum rate of energy by 250 kWh/m2, 450 kW/m2 and 700 kW/m2 for direct, defused and total radiation respectively (Fig.13.). Fig. 13. Radiation Analysis in Tabriz City. BM The Blue-mosque (Göy Məsçit in Azerbaijani language) of Tabriz was built in order of Jahan-Shah (Turkish king from of Qara-Qoyunlular) in 1448 AC (Fig. 14.). Its architectural style in Azerbaijani architecture categorized in the architectural school of Tabriz I (Ouria, 2015). It is the masterwork of Azerbaijani styles in Iran. It should be mentioned that the majority of masterworks in ancient Azerbaijan-Iran follow their climatic condition by implementing different techniques, elements, and materials. Fig.14. BM Determining the Geometric Functions of Domes The size of each element is estimated in field surveying. The form of the building consists of two cubes (8.7m) in height. Also, there are thirteen domes on its roof. The similar domes are arranged into the same category. These domes are categorized in Fig. 15. Fig. 15. Classification Plan According to the method of Lagrange interpolation (Eque 33), the equation of each class of domes in the BM is defined to estimate the rate of heights h(x) in different points (x). The equation of elements defines its height range according to horizontal dimension (x), which makes it possible to compute surface area. The results of the analyzed diagrams of the classification plan are presented in table 10.

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