Optimal Combination of External Wall Insulation Thickness and Surface Solar Reﬂectivity of Non-Residential Buildings in the Korean Peninsula

: To delay fossil energy depletion and implement the Paris Climate Change Accord, the South Korean government is attempting to reduce greenhouse gas emissions with the establishment of the 2030 Roadmap. The insulation performance of external walls is being continuously enhanced in the architectural domain. However, Korea’s policy and construction market focuses only on the heat resistance of buildings’ external walls to enhance the insulation performance, leading to an increased thickness of the insulation materials. In this study, the relationship between the surface reﬂectivity and insulation thickness of external walls was examined to formulate an effective insulation strategy for buildings in Korea. Ofﬁce buildings of 12 regions in the Korean Peninsula were considered. The dynamic energy simulation program EnergyPlus was used to perform the heating and cooling load analyses. The present worth method was adopted to perform the economic analysis. The analysis of the cooling and heating loads indicated that a change occurred not only in terms of the latitude but also between the Eastern and Western regions. The energy consumption could be reduced by increasing the reﬂectivity in the Southern region and lowering the reﬂectivity in the Northern region, based on the total load. In addition, a higher latitude corresponded to a higher energy saving effect owing to the increased insulation thickness. In the case of Jeju Island and Busan, regions with a relatively large cooling load and small heating load, the total load is little affected by insulation thickness at high reﬂectivity. If the external skin was considered to have the optimal reﬂectivity, the regions for optimal insulation thickness could be divided into three categories: north, central and south.


Introduction
Among OECD countries, South Korea ranks first in terms of the increase in greenhouse gas emissions [1] (increase of 113% since 1990). To prevent energy depletion and implement the Paris Climate Change Accord, the National Greenhouse Gas Reduction Goals 2030 Roadmap was formulated by the government of the Republic of Korea in 2016. The objective is to reduce 37% (domestic 32.5%, overseas 4.5%) of the emissions compared to those in business as usual (BAU) conditions in the industry, home, commerce, public, and transportation domains. According to the roadmap, the industrial domain requires the highest reduction in the emissions (from 481.0 to 382.4 million tons of CO 2 ), with a reduction rate of 20.5%. Nevertheless, the architectural domain requires the highest rate of reduction (from 197.2 to 132.7 million tons, 32.7%) compared to the BAU conditions [2] to minimize the impact on the social economy. Moreover, only limited approaches are available to enhance the energy efficiency after construction, and most buildings have a long life span. Therefore, the formation of buildings with a high energy efficiency has become a key administrative purpose for the nation [3].
Since September 2013, the Korean government has expanded the scope of the energy saving plan submission. It is mandatory to submit an application to obtain a building permit with a floor area of 500 m 2 or more, to change the use or report, or to change the contents of the building register. The energy saving plan of a building consisted of mandatory (21 items in the architectural, mechanical and electrical sectors) and recommendation aspects, along with the energy performance index (EPI) (40 items in the architectural, mechanical, electrical and renewable sectors). All the mandates were required to be met, and the recommendations required a score of 65 or higher (74 for public buildings) to obtain the approval of a building. Especially, insulation (one of different mandatory energy saving plans) has been strengthened the most so far because appropriate insulation can reduce the energy consumption by approximately 40% to 70% compared to non-insulation cases, depending on the region and climate [4,5]. The basic points (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34) of the average thermal transmittance of the wall were allocated the largest proportion of the total points in the recommendation section. Thus, the applicant was encouraged to maintain a high insulation performance. The standard for the heat transmission rate of building sites by region was divided into four climates and applied accordingly (the divisions for the climate were increased from three to four in September 2018). Buildings in a higher latitude required a higher insulation performance. Figure 1 represents the insulation criteria for the external walls of non-residential buildings in the Korean Peninsula, in the central region. The x-axis indicates the revision year, and the y-axis shows the legal thermal transmittance criteria. The heat insulation criteria have become more stringent with time. Currently, Korea's standard for thermal transmittance has been revised to the level of passive house. long life span. Therefore, the formation of buildings with a high energy efficiency has become a key administrative purpose for the nation [3]. Since September 2013, the Korean government has expanded the scope of the energy saving plan submission. It is mandatory to submit an application to obtain a building permit with a floor area of 500 m 2 or more, to change the use or report, or to change the contents of the building register. The energy saving plan of a building consisted of mandatory (21 items in the architectural, mechanical and electrical sectors) and recommendation aspects, along with the energy performance index (EPI) (40 items in the architectural, mechanical, electrical and renewable sectors). All the mandates were required to be met, and the recommendations required a score of 65 or higher (74 for public buildings) to obtain the approval of a building. Especially, insulation (one of different mandatory energy saving plans) has been strengthened the most so far because appropriate insulation can reduce the energy consumption by approximately 40% to 70% compared to non-insulation cases, depending on the region and climate [4,5]. The basic points (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34) of the average thermal transmittance of the wall were allocated the largest proportion of the total points in the recommendation section. Thus, the applicant was encouraged to maintain a high insulation performance. The standard for the heat transmission rate of building sites by region was divided into four climates and applied accordingly (the divisions for the climate were increased from three to four in September 2018). Buildings in a higher latitude required a higher insulation performance. Figure 1 represents the insulation criteria for the external walls of non-residential buildings in the Korean Peninsula, in the central region. The x-axis indicates the revision year, and the y-axis shows the legal thermal transmittance criteria. The heat insulation criteria have become more stringent with time. Currently, Korea's standard for thermal transmittance has been revised to the level of passive house. The status of zero-energy building has become mandatory for public buildings since 2020 in Korea. Specifically, the primary energy output and primary energy consumption of the buildings are evaluated, and the buildings are assigned five grades according to the energy independence ratio. The Green Building Construction Support Act No. 16418, 2020.1.1. enforcement, is applied to public buildings subject to the submission of energy saving plans with a total floor area of 1000 m 2 or more, which are newly constructed, rebuilt, or annexed to public buildings. Moreover, although the foregoing is not applied to multi-family housing and dormitories, zero-energy conditions will be required for all private buildings after 2025 [6].
According to this background and policy situation, the importance of insulation performance, which accounts for the largest proportion of building energy saving factors, is expected to increase in Korea. However, to enhance the insulation property of external walls according to Korea's policy and construction market, most external walls are designed and produced with a focus on the heat resistance, which inevitably increases the thickness of the insulation. Although the performance enhancement of these resistive insulation materials can help effectively reduce the heating load, the cooling load cannot be  The status of zero-energy building has become mandatory for public buildings since 2020 in Korea. Specifically, the primary energy output and primary energy consumption of the buildings are evaluated, and the buildings are assigned five grades according to the energy independence ratio. The Green Building Construction Support Act No. 16418, 2020.1.1. enforcement, is applied to public buildings subject to the submission of energy saving plans with a total floor area of 1000 m 2 or more, which are newly constructed, rebuilt, or annexed to public buildings. Moreover, although the foregoing is not applied to multi-family housing and dormitories, zero-energy conditions will be required for all private buildings after 2025 [6].
According to this background and policy situation, the importance of insulation performance, which accounts for the largest proportion of building energy saving factors, is expected to increase in Korea. However, to enhance the insulation property of external walls according to Korea's policy and construction market, most external walls are designed and produced with a focus on the heat resistance, which inevitably increases the thickness of the insulation. Although the performance enhancement of these resistive insulation materials can help effectively reduce the heating load, the cooling load cannot be reduced [7]. Consequently, alternatives must be adopted to reduce the cooling loads in summer. The cooling load can be reduced by using cooling colors and cold paint by increasing the solar reflectivity of the external surface [8]. Moreover, the reflectivity of the Sustainability 2021, 13, 3205 3 of 24 external surface, when suitably combined with the existing insulation, can help improve the indoor thermal comfort and effectively reduce heating and cooling loads [9]. Therefore, in this study, the changes in the cooling, heating and total loads in 12 regions of the Korean Peninsula due to changes in the thickness of the external wall insulation material and the reflectivity of the external wall surface were examined to identify the energy saving strategies for each region. These strategies are expected to be used efficiently in the building design stage. In addition, by performing an economic analysis based on the combination of the insulation thickness, reflectivity and energy consumption, the optimal combination of the external wall insulation thickness and reflectivity for each region was derived to facilitate the establishment of a unified insulation strategy for Korea.
Existing studies on the effect of the reflectivity and insulation thickness of buildings' external walls on changes in heating and cooling loads have been surveyed. Many studies have focused on roofs among the external surface of buildings, likely because the application to the roof is more effective than that to a wall [9].
The studies pertaining to the reflectivity and insulation thickness of roofs can be summarized as follows: Ascione et al. [8] considered the penalties during heating periods due to roof reflectivity in the Mediterranean climate. Materials with four reflectivity values were evaluated. EnergyPlus simulations were conducted on four typical offices in Lisbon (Portugal), Seville (Spain), Naples (Italy) and Athens (Greece) to examine the effects of the insulation thickness and reflectivity combinations. It was concluded that an insulation of 12 to 14 cm must be adopted in all cities to avoid penalties during heating periods. Sabe et al. [10] assessed the energy performance according to the insulation thickness and reflectivity (white or black) of the roof in hot, humid climatic conditions in Saudi Arabia. It was observed that if a white roof were applied to a building, the use of insulation on the roof could be reduced. These results were expected to help upgrade Saudi architecture codes. Saafi et al. [11] derived the optimal combination of the roof insulation and cooling through life cycle cost analyses for residential buildings in Tunisia. The annual energy requirement was obtained using EnergyPlus and considering two roof structures, three insulation materials and three reflective scenarios. In Tunisia, the benefits of increasing the roof reflectivity in summer were greater than winter penalties, and a higher reflectivity was desirable. Ramamurthy et al. [12] quantified the heat transmitted over a year through the roof in northeastern United States. The objective was to identify the optimal combination of the roof reflectivity and insulation thickness to minimize the energy consumption. For the New York Metro, the albedo was 0.6, and the ideal insulation thickness was 46 cm; the heating and cooling loads could be considerably reduced when adopting these specifications. The white-roofed winter penalty was insignificant compared to the summer benefits. However, increasing the thickness of the roof insulation was expected to increase the cost recovery period, and the authors indicated that the roof life (20 years) must be considered as well. If the thickness of a 5.08 cm (2 in.) insulation was doubled, 13 years were required to recover the additional costs incurred.
The research on exterior walls has been primarily focused on determining the optimal insulation thicknesses for each region and use case worldwide [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]: Ozel [15] studied the optimal insulation thickness for structural materials on the southern walls of buildings in Turkey. Dynamic simulations were performed considering five structural materials (concrete, briquet, brick, blokbims and autoclaved aeration) and two insulation materials (extruded polystyrene (XPS) and extended polystyrene (EPS)). In addition, an economic analysis of the energy consumption costs (10 years) was performed to determine the optimal insulation thickness. The optimal insulation thickness was 2-8.2 cm, leading to energy savings of 2.78 to 102.16 $/m 2 and payback periods of 1.32 to 10.33 per year. Daouas et al. [18] determined the optimal insulation thickness of the external wall of a Tunisian building. The most profitable specifications corresponded to stone/brick sandwich walls and foam polystyrene as the insulation material, and the optimal insulation thickness was 5.7 cm. Wati et al. [19] examined the effects of external shading on the optimal insulation thickness of building walls in tropical areas. Increasing the shading reduced the optimal thickness, which was dependent on the directions. For each 1% reduction of solar radiation, the optimal insulation thickness was reduced by 0.035-0.036 cm in the south, east, and west regions, and 0.029 cm in the north. Furthermore, only a few studies attempted to analyze the cooling and heating loads through the external walls by correlating the reflectivity and insulation thickness: Ouarda Mansouri [26] investigated and analyzed the reflective coating effect and performance of external walls of residential buildings in the Mediterranean climate zone of Algeria with the TRNSYS analysis program. The results showed that the presence of insulation combined with a high solar reflectivity positively influenced the indoor air, thermal comfort levels and energy efficiency, providing a better environment for residents. The optimal combination corresponded to a wall of light-colored coatings with an albedo higher than 0.5 with insulation. Yuan [27] investigated the optimal reflectivity and insulation thickness by region in Japan. Based on the Japanese architectural market and economic analysis data, Yuan analyzed the changes in the cooling and heating loads according to the insulation thickness and reflectivity of each region and derived the optimal combination of the insulation thickness and reflectivity by region considering the cost. The results were Naha 0-10 mm, 0.7-1.0; Fukuoka 50 mm, 0.5-0.6; Osaka 60 mm 0.5-0.6; Nagoya 60 mm, 0.5-0.6; Tokyo 70 mm, 0.4-0.5; Sapporo 100 mm, 0-0.1. In this work, the study of Yuan was referenced, and the differences between this work and Yuan's research are summarized in Table 1.

Materials and Methods
The cooling and heating loads of buildings for each region were determined using EnergyPlus after selecting representative cities from low to high latitudes of the Korean Peninsula.
After collecting the simulation results and data, an economic analysis was conducted using the present worth method. Figure 2 shows the process flow of this study.

Materials and Methods
The cooling and heating loads of buildings for each region were determined using EnergyPlus after selecting representative cities from low to high latitudes of the Korean Peninsula.
After collecting the simulation results and data, an economic analysis was conducted using the present worth method. Figure 2 shows the process flow of this study.

Representative City
Each region has different climatic characteristics depending on the latitude and surrounding environment. This aspect directly influences the energy load of a building. To reflect the diversity of the entire Korean Peninsula, 12 cities-from Jeju Island, located at a low latitude, to Chongjin, at a high latitude-were selected as representative cities (in the order of population size). Figure 3 shows the location of the cities selected on the map of the Korean Peninsula. The Korean Peninsula is situated in the temperate climate zone of the mid-latitude region and exhibits four distinct seasons: spring, summer, fall and winter. Winter is cold and dry and influenced by the dry continental high pressure. In summer, the hot weather is affected by the hot and humid North Pacific high pressure. Spring and fall show many clear and dry days due to the influence of the migratory anticyclone. The geographical information and detailed weather characteristics of each region of the Korean Peninsula are summarized in Table 2, according to the Korea Meteorological Administration data [28] and a literature survey [29][30][31][32].  Each region has different climatic characteristics depending on the latitude and surrounding environment. This aspect directly influences the energy load of a building. To reflect the diversity of the entire Korean Peninsula, 12 cities-from Jeju Island, located at a low latitude, to Chongjin, at a high latitude-were selected as representative cities (in the order of population size). Figure 3 shows the location of the cities selected on the map of the Korean Peninsula.     The Korean Peninsula is situated in the temperate climate zone of the mid-latitude region and exhibits four distinct seasons: spring, summer, fall and winter. Winter is cold and dry and influenced by the dry continental high pressure. In summer, the hot weather is affected by the hot and humid North Pacific high pressure. Spring and fall show many clear and dry days due to the influence of the migratory anticyclone. The geographical information and detailed weather characteristics of each region of the Korean Peninsula are summarized in Table 2, according to the Korea Meteorological Administration data [28] and a literature survey [29][30][31][32].  It can be noted that the average annual temperature (based on the average values from 1981 to 2010) decreased toward higher latitudes. (Gangneung, which faces the east coast and is affected by coastal climate, was not considered). The highest average temperature, 19.5 • C, corresponded to Daegu, which has the characteristics of a basin. The lowest average temperature, 4.5 • C, corresponded to Chongjin, which is located in the high latitude of the Korean Peninsula. As of 2016, the highest temperature in most cities in the Korean Peninsula occurred in August (Jeju in July) and the lowest temperature occurred in January.

Selection of Simulated Buildings
The simulation buildings were selected as medium-sized standard buildings for non-residential work facilities [33], as extracted from the 2019 Energy Efficiency Rating DB Analysis (2016-2018). The selected standard building has a floor area of 6147 m 2 , five stories above ground, two basement floors with reinforced concrete and a southward-facing orientation. The details of the building are presented in Figure 4 and Table 3. Figure 4 is a simplified zone layout for the middle floor based on the standard model of reference [33]. The zone ratio is given in Table 3. For the zone ratio in Table 3, others include spaces for the office occupants, such as restrooms, rest area, etc. The first floor usually houses generally convenient facilities for the neighborhood. Table 3. Details of a standard office (medium-sized) building model in Korea [33].

Item Detail
Building scale Total floor area: 6147 m 2 (five floors above ground, two basement levels)   Table 3. Details of a standard office (medium-sized) building model in Korea [33].

Item Detail
Building scale Total floor area: 6147 m 2 (five floors above ground, two basement levels) The external wall structure is based on the reinforced concrete structure of the standard building. The external wall finish reflects the exterior insulation finishing system and involves an aluminum sheet finish. Currently, such buildings are widely used as nonresidential office facilities in Korea. The detailed composition of the external wall structure is illustrated in Figure 5. The external wall structure is based on the reinforced concrete structure of the standard building. The external wall finish reflects the exterior insulation finishing system and involves an aluminum sheet finish. Currently, such buildings are widely used as nonresidential office facilities in Korea. The detailed composition of the external wall structure is illustrated in Figure 5.

Energy Simulation
A total of 1620 simulations (135 times per region) were performed using EnergyPlus ver. 8.9, a dynamic energy simulation program, for the selected standard buildings, considering 12 regions of the Korean Peninsula, to calculate the cooling and heating demand and the energy consumption. The simulation conditions are summarized in Table 4 In general, the heat transfer through the external wall must be calculated to determine the optimal insulation thickness [34,35]. In most studies, this analysis is performed using the degree-time method (degree-day or degree-hour). This approach is a simple  Table 4.
In general, the heat transfer through the external wall must be calculated to determine the optimal insulation thickness [34,35]. In most studies, this analysis is performed using the degree-time method (degree-day or degree-hour). This approach is a simple technique pertaining to the steady state [20,[36][37][38][39][40][41][42]. However, the degree-time method, in most cases, does not take into account the non-constant operation schedule (lighting, occupancy and equipment), the heat storage effect of walls and the characteristics of the heating and cooling system in the calculation of the heat transfer through the external wall [43]. In this regard, a dynamic heat transfer simulation program can calculate the building energy consumption more accurately.
The EnergyPlus software is a powerful dynamic energy simulation engine, which was used to realize the official thermal modeling of the US Department of Energy. Moreover, Design Builder (6.1.4.006) was used for building modeling. The accuracy of EnergyPlus has been demonstrated by the International Energy Agency in accordance with the Building Energy Simulation TEST (BESTest) procedure [44]. To calculate the amount of energy required to satisfy the heating and cooling demand in the simulation building, the Energy-Plus software utilized many program modules that operated simultaneously. This software calculates the heat load according to the thermal balance method, which can take into account the climatic characteristics over time, thereby considering the complete thermal balance of the inner and outer surfaces and the transient heat conduction through the building [45,46]. In this study, the time step was set as 30 min. The detailed equations and more information are available in the EnergyPlus Engineering Reference Document [47].
The climate data were based on data from TMYx (Typical Meteorological Years 2004-2018) for 12 regions of the Korean Peninsula. The TMYx file involves the typical metering data derived from hourly meteorological data from the US NOAA's Integrated Surface Database through 2018, by using the TMY/ISO 15927-4: 2005 methodology, and currently provides more than 13,550 TMYx locations [48]. The goal is to provide a standardized weather file format for solar system calculations. The basic logic of the TY type weather file is that it represents long-term weather conditions with data containing the least weather points, and thus the data correspond to the weather data closest to the long-term average of the climate [49]. Therefore, the typical year type weather files are used to estimate the average energy consumption [50].
The influence of the surrounding buildings affects the heating and cooling loads of buildings. However, it was difficult to generalize this effect, and it was not reflected in this study. Moreover, because the simulations were conducted considering the middle floor of the building, the upper and lower floors were set as adiabatic. Figure 6 show the 3D modeling of the simulated space. this study. Moreover, because the simulations were conducted considering the middle floor of the building, the upper and lower floors were set as adiabatic. Figure 6 show the 3D modeling of the simulated space. The simulation parameters include the reflectivity and insulation properties of the external wall. The reflectivity and insulation properties of the buildings in each region were changed for the external walls of the east, west, south and north. For the input range, the reflectivity was varied in nine steps from 0.1 to 0.9 in intervals of 0.1. Moreover, the insulation was varied in 15 steps from 10 mm to 150 mm in 10 mm intervals. The input The simulation parameters include the reflectivity and insulation properties of the external wall. The reflectivity and insulation properties of the buildings in each region were changed for the external walls of the east, west, south and north. For the input range, the reflectivity was varied in nine steps from 0.1 to 0.9 in intervals of 0.1. Moreover, the insulation was varied in 15 steps from 10 mm to 150 mm in 10 mm intervals. The input conditions for the simulation are summarized in Table 4. Except for these values, the default values were used.

Cost Analysis
For the cost analysis, the present worth method was used, in which all future costs are compared and analyzed by converting them into current costs. The total cost consists of the insulation cost (C i ), reflectivity material cost (C r ) and present value (C e ) of the energy cost over the life of the building and can be calculated as a sum of all these costs [56] as follows: (1) C i was calculated by multiplying the cost per unit area (C im ) of the insulation by the required area (A i ). C r was calculated by multiplying the cost per unit area (C rm ) of the reflector by the required area (A r ). C The cost survey of insulation and reflective materials was conducted considering the Korean architectural market. The costs included material and labor. Specifically, the survey was conducted based on the information of commodity prices, Korea's price information and company estimates, and the lowest price among these aspects was selected. In addition, the advice of a construction specialist was sought to obtain a unit cost of the external wall construction.
Labor costs were divided into two categories based on 100 mm, and each sector corresponded to a certain cost. Specifically, sectors over 100 mm costed an additional $1.76 per m 2 , due to the increase in the material weight and volume. The expenses were 1% of the workforce cost based on the standard calculation of the construction works and the external insulation work method published in 2019 [57].
According to an investigation by curtain wall experts and companies, the reflectivity of 0.1-0.7 of the external wall can be adjusted by painting the aluminum sheet surface without any additional cost. However, the reflectivity of 0.8 or higher is difficult to implement using pure aluminum materials or paint alone, as this process is expected to incur additional costs. In this study, this range was excluded from the cost analysis because the reflectivity of 0.8 or higher is rarely used in the Korean construction market as an outer finish material, and the market prices are not available.
The present value (C e ) of the energy costs during the lifetime of a building can be calculated by multiplying the total energy cost (E t ) per unit area per year by the target floor area (A f ) and a present worth factor (PWF), as expressed in Equation (4).
E t can be obtained as the sum of the cost of cooling energy per unit area and heating energy per unit area per year (Equation (5)). The cost of cooling energy per unit area per year was calculated by multiplying the annual cooling energy consumption (E c ) per unit area, calculated by an energy simulation, and the 2020 Korean electricity fee (summer) (F s ). The annual heating energy cost per unit area was calculated by multiplying the annual heating energy consumption (E h ) per unit area, calculated by an energy simulation, and the 2020 Korean electricity fee (winter) (F w ). The annual cooling and heating energy consumption per unit area were calculated through the simulation by reflecting the cooling and heating coefficient of performance (COP) of the EHP according to the demand for heating and cooling.
The PWF was calculated based on the building's life (n), inflation rate (I f ) and interest rate (I t ). The basic expression is given as Equation (6), where r can be obtained in terms of the interest rate and inflation ratio as the actual interest rate. If the interest rate is greater or smaller than the inflation, Equations (7) and (8) are used, respectively. Equation (9) may be used when the two values are identical [18][19][20]39,56,[58][59][60]. In this study, Equation (7) was used because the interest rates were higher than the inflation rates, and the cost analysis period was considered to be 40 y, based on the standard life of the Korean corporate tax law buildings. Table 5 summarizes the conditions considered for the cost analysis in this study.

PWF =
(1 + r) n − 1 r(r + 1) n (6) For I t = I f , PWF = n 1 + I t (9)  Table 6 shows the HDD (Heating degree day) and CDD (Cooling degree day) of representative cities based on a temperature of 18.3 • C. These values can approximately quantify the demand of energy needed to heat or cool buildings for each location. The thermal load was calculated by reflecting the climate of 12 regions by using EnergyPlus for the middle floor of the building, which occupies a relatively large portion of the building. The heat load changes due to the change in the insulation thickness and the reflectivity of the external walls could be clarified, as follows.

Cooling Load Results
The analysis results for the cooling load are as follows:

•
In general, the cooling load decreases as the latitude increases, although certain differences were observed between the east and west regions of the Korean Peninsula, (East region: Busan, Daegu, Gangneung, Hamhung and Chongjin. West Region: Jeju, Kwangju, Daejeon, Seoul, Kaesong, Pyongyang and Sinuiju) • Even when the cities are located at a similar latitude, less cooling load occurs in the east than that in the west. For example, Kwangju and Busan, Seoul and Gangneung and Sinuiju and Hamhung are located at similar latitudes, but there are less cooling loads in the east compared to the west, likely because of the coastal climate effects in the east.

•
As the reflectivity increases, the cooling load decreases [10,11,65]. This phenomenon occurs because the increase in the reflectivity of the solar radiation energy prevents the temperature rise of the external wall, thereby reducing the amount of heat transfer to the indoor space [24,25].

•
As the thickness of the insulation material increases, there exists a sector in which the cooling load increases. This phenomenon occurs because increasing the thickness of the resistive thermal insulation results in less heat loss to the outside that was generated internally by the equipment, the lighting, the human body and solar radiation [66][67][68][69][70]. These phenomena can be identified by the change in the cooling load, i.e., the slope, against the change in the insulation thickness. In this study, the change of insulation thickness for each reflectivity was constant at 10 mm; therefore, if the change in the cooling load was greater than zero, then this sector could be considered as one in which the cooling load increases with increasing insulation thickness. The changes in the cooling load occur over a larger range as the insulation thickness decreases in a thin sector (approximately 10 to 40 mm) and the reflectivity of the external wall increases.

•
As the reflectivity of the exterior wall of the building increases, the region with a relatively large reduction in cooling loads pertains to the low latitudinal region. Therefore, the cooling load can be effectively reduced by increasing the external wall reflectivity at low latitudes.
To reduce the cooling load, it is necessary to increase the surface reflectivity of the external wall in the same way as Ouarda Mansouri's study [26] of the Mediterranean climate zone of Algeria and adopt an appropriate insulation thickness to achieve the corresponding reflectivity. To reduce the cooling load for each region in the Korean Peninsula, Figure 7 indicates the appropriate insulation thickness according to the reflectivity of the external wall surface. reflectivity at low latitudes.
To reduce the cooling load, it is necessary to increase the surface reflectivity of the external wall in the same way as Ouarda Mansouri's study [26] of the Mediterranean climate zone of Algeria and adopt an appropriate insulation thickness to achieve the corresponding reflectivity. To reduce the cooling load for each region in the Korean Peninsula, Figure 7 indicates the appropriate insulation thickness according to the reflectivity of the external wall surface.

Heating Load Results
The results of the analysis of the heating load are as follows.


There exist certain differences between the eastern and western regions of the Korean Peninsula; however, in general, the heating load decreases at lower latitudes.  The heating load is smaller in the eastern than in the western region of the Korean Peninsula. For example, Chongjin, Hamhung, Gangneung and Busan, located in the

Heating Load Results
The results of the analysis of the heating load are as follows.
• There exist certain differences between the eastern and western regions of the Korean Peninsula; however, in general, the heating load decreases at lower latitudes.

•
The heating load is smaller in the eastern than in the western region of the Korean Peninsula. For example, Chongjin, Hamhung, Gangneung and Busan, located in the east, are located at a higher or almost identical latitude than Sinuiju, Pyongyang, Daejeon and Kwangju, which are located in the west, but exhibit a smaller heating load. This phenomenon likely occurs because the western part of the Korean Peninsula is affected by the continental climate, and the eastern part has the characteristics of the coastal climate caused by the Kuroshio current [28].

•
As the reflectivity increases, the heating load increases. This phenomenon occurs because as the external wall reflectivity increases, the solar radiation energy absorbed by the external wall decreases.

•
The increase in the insulation thickness decreases the heating load because less heat is lost to the outside [71-73].

•
The heating load changes considerably in the thin sector (10 to 40 mm) of the insulation. As the thickness of the insulation increases, this value decreases rapidly. As the reflectivity increases or the thickness of the insulation decreases, the heating load increases.

•
The change in the amount of reduction in the heating load due to the increase in the insulation material increases as the latitude increases. Therefore, the heating load reduction effect pertaining to the increase in the insulation thickness is more notable at higher latitudes than that at lower latitudes.
To reduce the heating load, one must reduce the reflectivity of the external wall and increase the insulation thickness. To reduce the heating load for each region, Figure 8 shows the insulation thickness suitable for a certain reflectivity of the external wall.


The heating load changes considerably in the thin sector (10 to 40 mm) of the insulation. As the thickness of the insulation increases, this value decreases rapidly. As the reflectivity increases or the thickness of the insulation decreases, the heating load increases.  The change in the amount of reduction in the heating load due to the increase in the insulation material increases as the latitude increases. Therefore, the heating load reduction effect pertaining to the increase in the insulation thickness is more notable at higher latitudes than that at lower latitudes.
To reduce the heating load, one must reduce the reflectivity of the external wall and increase the insulation thickness. To reduce the heating load for each region, Figure 8 shows the insulation thickness suitable for a certain reflectivity of the external wall.  The cooling and heating load analysis shows that insulation thickness and reflectivity yield different results. Therefore, the total amount of heating and cooling loads must be evaluated on a yearly basis, as explained in the following section.

Total Load Results
The regional cooling and heating loads described in the previous section indicate that the regions in which the annual cooling load is higher than the heating load are Jeju, Busan, Daegu, Kwangju, Daejeon and Gangneung, which are located at low latitudes or are strongly affected by the coastal climate. Moreover, the regions in which the annual heating loads are higher than the cooling loads are located at a high latitude or strongly affected by coastal climate, such as Seoul, Kaesong, Pyongyang, Hamhung, Sinuiju and Chongjin. To reduce the load on buildings, a larger amount of solar radiation should be absorbed in winter, and a high reflectivity should be maintained in summer [25,[74][75][76]. Therefore, this section clarifies the optimum insulation thickness and reflectivity through the total load on a yearly basis. Figure 9 shows the total changes in the cooling and heating loads by region according to the reflectivity and insulation thickness.
heating loads are higher than the cooling loads are located at a high latitude or strongly affected by coastal climate, such as Seoul, Kaesong, Pyongyang, Hamhung, Sinuiju and Chongjin. To reduce the load on buildings, a larger amount of solar radiation should be absorbed in winter, and a high reflectivity should be maintained in summer [25,[74][75][76]. Therefore, this section clarifies the optimum insulation thickness and reflectivity through the total load on a yearly basis. Figure 9 shows the total changes in the cooling and heating loads by region according to the reflectivity and insulation thickness. The following key findings could be derived:


The total load of each region can be clearly divided into the western part of the Korean Peninsula (Pyongyang, Sinuiju, Kaesong, Daejeon, Seoul, Kwangju) and the eastern part (Hamhung, Chongjin, Daegu, Gangneung, and Busan), with the western part occupying a larger portion. This finding occurs because the eastern part of the Korean Peninsula is affected by the coastal climate, involving a small daily temperature range and a mild climate. The following key findings could be derived: • The total load of each region can be clearly divided into the western part of the Korean Peninsula (Pyongyang, Sinuiju, Kaesong, Daejeon, Seoul, Kwangju) and the eastern part (Hamhung, Chongjin, Daegu, Gangneung, and Busan), with the western part occupying a larger portion. This finding occurs because the eastern part of the Korean Peninsula is affected by the coastal climate, involving a small daily temperature range and a mild climate.

•
The increase and decrease in the reflectivity are based on the different total loads by region. With an increased reflectivity, Chongjin, Sinuiju, Hamhung, Pyongyang and Kaesong exhibited an increased total load, while Jeju, Busan, Gangneung, Kwangju, Daejeon, Daegu and Seoul exhibited a decreased total load. The regions are listed in order of the increase and decrease in the load. Specifically, the regions with high heating load should have lower reflectivity and the regions with high cooling loads higher reflectivity, to reduce each load. In other words, energy saving can be achieved by increasing and decreasing the reflectivity in the southern and northern regions, respectively. • In all the regions, the total load decreases as the insulation thickness increases. • A higher latitude corresponds to a greater total load change due to the change in the insulation thickness. In other words, a higher latitude corresponds to a significant effect of the insulation thickness. • Lower-latitude regions correspond to a reduced total load variation against the change in the insulation thickness.

•
The total load is highly dependent on insulation thickness in the thin insulation thickness sector, but becomes less dependent in the thick sector.

•
In the case of Jeju Island and Busan, regions with relatively large cooling load and small heating load, the total load is little affected by insulation thickness at high reflectivity. Figure 9 can help select the appropriate insulation thickness depending on the reflectivity of the external wall to reduce the total load of each region.
The abovementioned load analysis indicated that relatively large variations in the load occur in the thin sector (10-40 mm) of the insulation [77][78][79]. Therefore, the optimal insulation thickness and reflectivity analysis must be performed considering the total cost of the whole year. This aspect is further evaluated in the following sections.

Optimal Insulation Thickness and Reflectivity Considering Economics
The optimal insulation thickness and reflectivity for each region refer to a combination of the reflectivity and the insulation thickness with the lowest total cost. The high-latitudelying Chongjin, mid-latitude-lying Seoul, and low-latitude-lying Jeju are considered as the representative regions of each latitude in the Korean Peninsula. Figures 10-12 show the optimum insulation thickness and reflectivity considering the total cost by region, exterior wall insulation and graph of the total cost change with the reflectivity change.   Figure 11 corresponds to Seoul, which is a representative region for mid-latitude regions, and the following findings can be derived:   Figure 11 corresponds to Seoul, which is a representative region for mid-latitude regions, and the following findings can be derived:


The shape of the total cost graph is similar to a U-shape.  The total cost is reduced as the insulation thickness increases from 10 to 50 mm; how-


The total cost decreases as the insulation thickness increases to 60 mm; however, it increases at higher thicknesses.  The change in the total cost with the change in reflectivity decreases as the thickness of the insulation increases. In particular, a relatively large change can be observed for the insulation thickness of 10-20 mm. In contrast to the low latitude case, a lower reflectivity corresponds to a lower total cost.  The lowest total cost combination pertains to an insulation thickness and reflectivity of 60 mm and 0.1, respectively. The analysis of the optimal insulation thickness and reflectivity for each region considering the total cost yielded the following trends according to the change in latitude.


High-latitude regions correspond to a higher shift to the right of the optimal insulation thickness.  The range of total cost due to changes in the insulation thickness varied for the high (approximately 157-172 $/m 2 ), low (approximately 140-152 $/m 2 ) and mid (approximately 163-172 $/m 2 ) latitudes. Therefore, if the high-latitude region, the building is assigned an optimum insulation thickness, and the insulation thickness for the low-  Figure 10 corresponds to Jeju, which is a representative region for low-latitude regions, and the following findings can be derived:

•
The total cost mimics the shape of a proportional graph. • Except for the insulation thickness of 10-20 mm, a thicker insulation corresponds to a higher total cost.

•
The change in the total cost for changes in the reflectivity at an arbitrary insulation thickness is relatively large compared to that in the other regions. High reflectivity corresponds to a minimum total cost for all insulation thicknesses. In particular, a thinner insulation corresponds to a greater change in the total cost. • The lowest total cost combination pertains to an insulation thickness and reflectivity of 20 mm and 0.7, respectively, for Jeju. Figure 11 corresponds to Seoul, which is a representative region for mid-latitude regions, and the following findings can be derived:

•
The shape of the total cost graph is similar to a U-shape.

•
The total cost is reduced as the insulation thickness increases from 10 to 50 mm; however, the cost in the subsequent sector increases.

•
The cost changes due to the changes in reflectivity are not as large as those in low latitudes. However, the thin sector of the insulation exhibits a relatively large change compared to that in the thick sector.

•
The lowest total cost combination pertains to an insulation thickness and reflectivity of 50 mm and 0.7, respectively. Figure 12 corresponds to Chongjin, which is a representative region for high-latitude regions, and the following findings can be derived:

•
The shape of the total cost graph is close to the L-shape.

•
The total cost decreases as the insulation thickness increases to 60 mm; however, it increases at higher thicknesses.

•
The change in the total cost with the change in reflectivity decreases as the thickness of the insulation increases. In particular, a relatively large change can be observed for the insulation thickness of 10-20 mm. In contrast to the low latitude case, a lower reflectivity corresponds to a lower total cost. • The lowest total cost combination pertains to an insulation thickness and reflectivity of 60 mm and 0.1, respectively.
The analysis of the optimal insulation thickness and reflectivity for each region considering the total cost yielded the following trends according to the change in latitude.

•
High-latitude regions correspond to a higher shift to the right of the optimal insulation thickness.

•
The range of total cost due to changes in the insulation thickness varied for the high (approximately 157-172 $/m 2 ), low (approximately 140-152 $/m 2 ) and mid (approximately 163-172 $/m 2 ) latitudes. Therefore, if the high-latitude region, the building is assigned an optimum insulation thickness, and the insulation thickness for the low-latitude building is not larger than the one required, and a relatively large energy saving effect can be expected compared to that in the mid-latitude.

•
In all the regions, the total cost changes are significant due to changes in reflectivity in the regions with a thin insulation thickness. This aspect can increase the energy savings in terms of the surface reflectivity in low-latitude regions, as the optimal insulation thickness occurs in sectors thinner than that in the other regions.

•
In the low latitude and mid latitude regions, a higher reflectivity corresponds to a lower total cost. However, in high latitudes, a lower reflectivity corresponds to a lower total cost.
Finally, for the 12 regions, the optimal insulation thickness and reflectivity can be derived, as illustrated in Figure 13.

Conclusions
By selecting 12 representative cities and the office building in the Korean Peninsula, this study was aimed at examining the changes in the cooling and heating loads due to the changes in the insulation thickness and reflectivity and at deriving the optimal insulation thickness and reflectivity considering the total cost. The cooling and heating load were calculated using the dynamic simulation program EnergyPlus. Moreover, a cost analysis was performed using the present worth method. The total cost includes the initial investment and energy cost during the analysis period.
The results of the analysis can be divided into three main categories: analysis of cooling and heating loads by region, analysis of total cost changes according to the optimal insulation thickness and reflectivity, and derivation of the optimal insulation thickness and reflectivity.


According to the analysis of heating and cooling loads in the Korean Peninsula, certain changes were observed in the eastern and western regions as well as the latitude.  To reduce the cooling load, it is necessary to increase the reflectivity of the external wall and adopt an insulation thickness suitable for that reflectivity. Figure 7 illus- • All the regions except Chongjin (reflectivity 0.1) and Sinuiju (reflectivity 0.5), which are located at high latitudes, exhibited the lowest cost when the reflectivity was high (reflectivity 0.7). Moreover, high-latitude regions with an optimal reflectivity of 0.7 corresponded to a larger optimal insulation thickness.

•
Comparing the optimal reflectivity values of the two countries based on Yuan's research data [27], regions close to the poles had optimal values in the range of low reflectivity, and regions close to the equator had optimal values in the range of high reflectivity. For the central region, the optimum reflectivity was 0.7 in the Korean Peninsula and 0.4-0.6 in Japan, although the two countries are located in similar latitudes.

•
When the regions are sorted in order of large cooling loads, in most regions, the optimum reflectivity is high in the order of large cooling loads. However, although Sinuiju exhibited a higher cooling load than Hamhung, it required a lower optimal reflectivity. In terms of the cooling load, Sinuiju exhibited values one step larger than those of Hamhung, but in terms of the heating load, Sinuiju exhibited values three step larger. Therefore, in the case of Sinuiju, the thickness of the insulating materials must be increased, and the reflectivity must be reduced to lower the heating load.

•
The high reflectivity of the external wall may reflect sunlight according to the reflective characteristics, creating a glare around the building and vehicle drivers [80,81]. Therefore, a high reflectivity of the exterior walls of the buildings must be accompanied by an environmental impact assessment considering the surrounding environment. • Sinuiju is located at a lower latitude than Chongjin but requires an optimal insulation thickness larger than that of Chongjin. This phenomenon is likely accompanied by an increase in insulation thickness because Sinuiju has a larger heating load than Chongjin. • In all regions, the thickness of the optimal insulation material increased in the order of the large heating loads.

•
Assuming that the optimal reflectivity is applied to the external wall, the regions for the optimal insulation thickness can be divided into three categories: Jeju and Busan (20 mm); Daegu, Kwangju, Daejeon, Seoul, Gangneung and Kaesong (50 mm); Chongjin, Sinuiju, Pyongyang and Hamhung (60 mm).

Conclusions
By selecting 12 representative cities and the office building in the Korean Peninsula, this study was aimed at examining the changes in the cooling and heating loads due to the changes in the insulation thickness and reflectivity and at deriving the optimal insulation thickness and reflectivity considering the total cost. The cooling and heating load were calculated using the dynamic simulation program EnergyPlus. Moreover, a cost analysis was performed using the present worth method. The total cost includes the initial investment and energy cost during the analysis period.
The results of the analysis can be divided into three main categories: analysis of cooling and heating loads by region, analysis of total cost changes according to the optimal insulation thickness and reflectivity, and derivation of the optimal insulation thickness and reflectivity.

•
According to the analysis of heating and cooling loads in the Korean Peninsula, certain changes were observed in the eastern and western regions as well as the latitude.

•
To reduce the cooling load, it is necessary to increase the reflectivity of the external wall and adopt an insulation thickness suitable for that reflectivity. Figure 7 illustrates the appropriate insulation thickness according to the reflectivity of the external wall of the building.

•
To reduce the heating load, one must reduce the reflectivity of the external wall and increase the insulation thickness. Figure 8 presents the insulation thicknesses suitable to match the reflectivity of the exterior walls by region.
The cooling and heating load analysis shows that the load reduction methods lead to certain variations. Therefore, it is necessary to analyze the total amount of heating and cooling loads on a yearly basis. The key results are as follows:

•
To reduce the total load, energy can be saved by increasing and decreasing the reflectivity in the southern region (South Korea) and northern region (North Korea), respectively.

•
The total load decreases as the insulation thickness increases in all regions. In particular, high-latitude regions present greater total load changes due to the change in the insulation thickness. • However, in the case of Jeju Island and Busan, which have relatively large cooling loads and small heating loads, a high reflectivity of the external walls corresponds to a small effect by the increase in the insulation thickness.
The optimal combination of insulation thickness and reflectivity based on the total cost, including the initial installation and energy costs, was studied. High-latitude Chongjin, mid-latitude Seoul and low-latitude Jeju were designated as representative regions for each latitude in the Korean Peninsula. For the minimum total cost, the combinations of insulation thickness and reflectivity are 20 mm, 0.7; 50 mm, 0.7 and 60 mm, 0.1 for Jeju, Seoul and Chongjin, respectively.
When the market price of the 0.8-0.9 sector of reflectivity is available in the Korean architectural outer finish market, an economic analysis of the high-reflection sector must be incorporated through additional cost investigations. Moreover, further research is needed for residential buildings because the building envelope of residential buildings is more important than that of the office buildings.

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Informed Consent Statement: Not applicable.

Conflicts of Interest:
The authors declare no conflict of interest.