A Time-Dependent Model for Predicting Thermal Environment of Mono-Slope Solar Greenhouses in Cold Regions

Most greenhouses in the Canadian Prairies shut down during the coldest months (November to February) because of the hefty heating cost. Chinese mono-slope solar greenhouses do not primarily rely on supplemental heating; instead, they mostly rely on solar energy to maintain the required indoor temperature in winter. This study focuses on improving an existing thermal model, entitled RGWSRHJ, for Chinese-style solar greenhouses (CSGs) to increase the robustness of the model for simulating the thermal environment of the CSGs located outside of China. The modified model, entitled SOGREEN, was validated using the field data collected from a CSG in Manitoba, Canada. The results indicate that the average prediction error for indoor and relative humidity is 1.9 °C and 7.0%, and the rRMSE value is 3.3% and 11.5%, respectively. The average error for predicting the north wall and ground surface temperature is 4.2 °C and 2.3 °C, respectively. The study also conducted a case study to analyze the thermal performance of a conceptual CSG in Saskatoon, Canada. The energy analysis indicates the heating requirement of the greenhouse highly depends on the availability of solar radiation. Besides winter, the heating requirement is relatively low in March to maintain 18 °C indoor temperature when the average outdoor temperature was below –4 °C, and negligible during May–August. The results indicate that vegetable production in CSGs could save about 55% on annual heating than traditional greenhouses. Hence, CSGs could be an energy-efficient solution for ensuring food security for northern communities in Canada and other cold regions.


Introduction
The extreme cold outdoor temperature is a major barrier to greenhouse production in cold regions. Supplemental heating and dehumidification have been commonly practiced in Canadian greenhouses. The heating cost could be around 70% to 85% of the total operating cost of crop production in greenhouses in high latitudes, excluding the cost associated with labor [1]. The heating cost in the Canadian greenhouse accounts for 10-35% of the total production cost [2,3]; therefore, most greenhouses in the Canadian Prairies shut down during the coldest months. The demand for local produce has increased over the last decade as more and more people acknowledge the health benefits of fresh vegetables and the need to reduce carbon emissions caused by long-distance transportation of fresh vegetables. Research indicates that the vegetables lose 15% to 77% of their vitamin C within a week of harvest [4]. Chinese solar greenhouses with a south mono-slope (CSGs) do not primarily rely on supplemental heating; instead, they are designed to maximize solar energy gain and minimize heat loss to maintain suitable indoor temperatures. Fortunately, the Canadian Prairies have extensive sunshine hours in a year, which provide favorable conditions for adapting CSGs and reducing heating cost as predicted by Ahamed et al. [5,6] 2 of 19 and Beshada et al. [7] through thermal modeling. Beshada et al. [7] conducted a field experiment in Elie, Manitoba, Canada, showing that CSGs is more energy-efficient for winter vegetable production in cold regions than traditional gutter-connected greenhouses. Ahamed et al. [8] simulated the heating requirement in a CSG located in Saskatoon, Canada, and found that it is about 50% of a gutter-connected greenhouse.
Many mechanistic models have been developed for simulating the thermal environment (temperature, RH, light intensity) of CSGs using MATLAB, CFD, FORTRAN, and VC++ methods [6,[9][10][11][12][13][14]. Most of these models are used to predict the diurnal variation of temperature [12,13,15] and humidity [14,16] inside the greenhouses. Zhang et al. [17] and Huang et al. [18] developed mathematical models to simulate the light environment (solar radiation) inside of CSGs. A few studies developed models for specific purposes, such as investigating the potential of renewable energy (solar and wind) to power the solar greenhouse [19], heat-pipe heating system [20], optimizing design parameters [21,22], etc. However, these models are not ready to use by industry, researchers, and growers. CFD (computation fluid dynamic)-based models [10,23] are reliable but require high computation capacity as well as a need to define the complicated boundary conditions [24]. A few studies [25][26][27] used commercial software, such as TRNSYS and EnergyPlus, to simulate the thermal environment of various types of solar greenhouses. However, most of these studies were conducted without considering the plant mass due to the complexity of modeling the dynamic nature of plant evapotranspiration, which is a primary component in energy balance. These commercial software packages are designed for building energy simulation, and thus, they need complicated modification to model the actual operation of greenhouses [25]. Some studies developed black-box models for CSGs using different approaches, such as the convex bidirectional extreme learning machine algorithm [16] and least squares support vector machine (LSSVM) with a particle swarm technique (PSO) for parameter optimization [28]. Zhang et al. [29] developed a model with a detailed 3D tomato canopy structure and simulated the micro light environment using a functional, structural plant model (FSPM). However, these black-box models have the limitation in terms of computation time and flexibility, and sometimes need to input some complicated unknown parameters. For example, the 3D model developed by Zhang et al. [29] needs a total running time of approximately 20 h to simulate results for 8 h using an Intel Core I7 CPU and 16 GB RAM. Additionally, many thermal models [5,[30][31][32] have been developed to simulate the microclimates of conventional greenhouses, which are not suitable for mono-slope greenhouses due to the differences in structures and environment control practices. Hence, a readily available mechanistic model (user-friendly software) with reasonable accuracy, low computational time, and various outputs (indoor temperature and RH, temperature of soil and north wall surface, and heating and cooling loads) would be a valuable tool for the design, optimization, and estimation of energy loads for CSGs.
Ma et al. [33] developed a software entitled RGWSRHJ for the dynamic simulation of the thermal environment of CSGs using finite difference numerical methods. This software could be a valuable tool for designers to compare and optimize CSG designs in China; however, it has many limitations for use outside of China. The major problem is that it is designed for Chinese CSGs, which usually lacks automated temperature control systems, so the indoor air temperature is constantly changing. The goal of the software is to predict the indoor thermal environment as a result of the passive impact of outdoor climatic conditions. In modern greenhouses, the practice is that the indoor temperature is controlled at its setpoint by heating and ventilation systems, and the goal of the thermal simulation is to analyze energy consumption under various indoor temperature and relative humidity (RH) set-points and ambient conditions, which the RGWSRHJ cannot do. Hence, the objective of this study was to modify the RGWSRHJ model into a new model named SOGREEN to predict the thermal environments (temperature and relative humidity) as well as the heating requirement of CSGs and validate the model using the data collected from a CSG in Canada. The SOGREEN model had many improvements to make it applicable to cold regions such as Canadian Prairies. Besides allowing supplemental heating prediction for maintaining the required set-point temperature, the other improvements include allowing polystyrene pellet insulation and double-layer inflated front-roof cover, resetting weather data type, modifying hourly simulation, adding sun blocker and internal thermal screen function, and converting the software in English. Finally, the SOGREEN model was used to analyze the thermal environment and heating requirement in a case study for a CSG in Saskatoon, Canada.
The article is organized into five sections. The literature review and knowledge gaps are presented in the introduction (Section 1). The model theory with the detailed mathematical formulation is described in Section 2. Section 3 describes the model formulation and steps for defining the building structures and control schedules, and the model validation is presented in Section 4. The results from the case study for the year-round operation of CSGs in the cold region (Saskatoon) are analyzed in Section 5. The final section contains the conclusions and future research direction for further development.

Model Theory
The SOGREEN model consists of five modules: the wall, ground, front roof covering material, ventilation, and evapotranspiration. The model was developed based on the heat balance of indoor air with consideration of all possible heat sources and sinks in CSGs. The differential Equation (1) reflects the sensible heat balance of the indoor air as affected by the greenhouse modules [21]: where ρ a is the air density (kg/m 3 ); C p is the air specific heat (J/kg· • C); V is the greenhouse volume (m 3 ); t i is the indoor air temperature ( • C); τ is the time (s); Q w is the heat gain (negative value is loss) from the walls and north roof (W); Q s is the heat released from the ground (W); Q g is the heat loss from the front roof (W); Q v is the heat loss through air exchange (W); and Q e is the heat loss by evapotranspiration (W). A two-dimensional unsteady state (dynamic) model that describes heat transfer through the composite envelopes (the walls, north roof, and ground) is given in Equation (2). As compared with the commonly used one-dimensional models, it reflects the heat transfer process more accurately: where λ is the heat conductivity coefficient (W/m· • C) and S is the heat from solar radiation per volume of the envelope material (W/m 3 ). Solar radiation is the primary heat source in the solar greenhouse. When sunshine strikes the walls, back roof, and ground surface in the daytime, their surface temperatures rise. After discretizing the control equation with the appropriate transformation, Equation (2) can be expressed as the following differential linear equations: ∆τ is the simulation step length (s); (∆y) j is the height of the node (i,j) (m); (∆x) i is the width of the node (i,j) (m); (δy) j is the center distance between the j and (j + 1) segment (m); (δx) i is the center distance between the node (i,j) and (i + 1,j) (m); λ i,j is the heat conductivity coefficient of the node (i,j), (W/m· • C); ρ i,j is the density of the node (i,j) (kg/m 3 ); C i,j is the specific heat of the node (i,j), (J/(kg· • C)); and SS i,j is the heat source of the node (i,j) (W/m 3 ).
The above linear equations set (3) can be written in the following matrix form: This tridiagonal matrix can be efficiently solved using the simplified form of Gaussian elimination known as the Thomas algorithm [34]. The solution of the above equations gives the transient temperature field of the wall, back roof, and ground. Based on the estimated temperature of the heat-storage component surfaces, the heat transfer from the wall, north roof, and ground to indoor air can be calculated by the flowing equations: where α i is the convective heat transfer coefficient between indoor air and surfaces (W/m 2 · • C); (∆y) j is the height of node (i,j) (m); L gh is the total length of greenhouse (m); t wsj is the surface temperature of the wall and back roof ( • C); and t ssj is the surface temperature of ground ( • C).
The heat loss through the transparent front roof, air exchange from infiltration and ventilation, and evapotranspiration can be estimated as follows [33]: where K is the heat transfer coefficient of the front roof (plastic film covering) (W/m 2 · • C); A f is the total area of the front roof (m 2 ); . V is the air exchange rate through ventilation and infiltration (m 3 /s); p ws is the saturated vapor pressure at room temperature (Pa); p w is the water vapor pressure at room temperature (Pa); K v is the coefficient of evapotranspiration per square meter of the ground area (kg/m 2 ·s·Pa); r is the latent heat of water vaporization (2442 kJ/kg); and A s is the indoor ground area (m 2 ).
The saturated vapor pressure and the water vapor pressure are estimated according to the ASHARE fundamental [35]. The air exchange rate is input through scheduling based on the time, crop species, and growth stages. Evapotranspiration is a dynamic process that depends on several factors including plant species, growth stages, indoor temperature, RH, and light intensity. The evapotranspiration coefficient of the crops needs to be selected based on crop density.

Model Development and Operation
As shown in Figure 1, the simulation process starts with the input of basic simulation conditions, including the location and weather conditions, physical and thermal properties of greenhouse structural materials, and operation schedule. Based on the input parameters, the model starts calculating the indoor thermal field for the next simulation step and recording each step's thermal parameters. When the simulation process comes to the final moment, the model compares the specified tracking point's temperature to the corre- sponding initial temperature and replaces the initial temperature with the predicted final temperature. After several simulation cycles, the fluctuation in indoor thermal parameters comes within the acceptable range (10 −5 , and the model will output the simulation results.  Figure 2 shows the initial interface of the simulation model. It contains weather condition settings, greenhouse constructional designs, materials selection for the envelope, indoor environment control parameters, etc. A save/load design function is added to simplify the operational process of the model. Different schedule modules are added for setting the operation schedules of the thermal blanket, supplemental heating, and ventilation systems. Moreover, a sun blocker function is added in the indoor control interface to reduce solar radiation entering the greenhouse in summer. An interior thermal screen function is added to reduce heat loss when the exterior thermal blanket fails to work because of mechanical failure or frozen blankets. The sun blocker and interior thermal screen are essential for cold regions to reduce greenhouse heating or cooling during the summer and winter seasons. -179°-179° E) and increases the wind speed limit up to 17 m/s to suit Canadian weather conditions.

Figure 2. Starting interface of the SOGREEN model.
The next step is to set the solar greenhouse design conditions, including the structural information, plant information, and building materials properties. For the south roof, besides plastic films, the modified model allows the option for glass, polycarbonate board, and other newly developed energy-efficient glazings, such as polystyrene (PS) pellet insulation and double-layer inflated film. The heat transfer coefficient of the PS pellet insulation is considered at 4.0 W/m 2. K for the daytime and 0.3 W/m 2. K at night. The overall heat transfer coefficient of a 6-cm thick double-layer inflated plastic film cover is 4.45 W/m 2. K, which slightly higher than the value (4.0 W/m 2. K) from the ASABE standard [36]. The aging factor may affect the rate of light transmission through the glazing materials; thus, the SOGREEN model allows users to select the degree of aging based on their judgment. The thermal blanket is an important measure to reduce the nighttime heat loss from the greenhouse, so a wide range of thermal properties for the thermal blanket is provided in the model from 3.0 to 0.5 RSI. The ground floor condition and the wetness level can affect the evaporation rate and the indoor thermal environment; therefore, users also need to select floor types, such as soil, mulch, concrete, and wetness level. Based on the plant condition, users need to choose plant density options: very sparse, sparse, ordinary, dense, and very dense. The plant transpiration is estimated based on the plant mass per unit area, which depends on the plant species and density information. Finally, the plant height and distance from the north wall are used to calculate the north wall's shaded area.
The next step is to define the physical and thermal properties of constructional materials for the greenhouse. The dimensions and building materials are set for the north roof, north wall, and floor. As shown in Figures 3 and 4, users input the segment lengths in the north wall and the building material's thermal properties, including density, thermal conductivity, and specific heat. The model also has a built-in material library that facilitates users to find commonly used materials. Figure 4 shows the interface of the greenhouse's detailed physical and thermal properties. The first step in simulation is to define the outdoor weather conditions. The user may select one of the three types of weather data, including user-defined weather data, measured weather data, and built-in weather data. The built-in weather data only includes several Chinese cities. The standard weather data, i.e., the typical meteorological year data (TMYD), were added to the user-defined module in this study. The simulation period, location (latitude and longitude), and elevations are also input in the weather condition interface. The SOGREEN model is extended to higher latitudes and longitudes (0 • -90 • N, −179 • -179 • E) and increases the wind speed limit up to 17 m/s to suit Canadian weather conditions. The next step is to set the solar greenhouse design conditions, including the structural information, plant information, and building materials properties. For the south roof, besides plastic films, the modified model allows the option for glass, polycarbonate board, and other newly developed energy-efficient glazings, such as polystyrene (PS) pellet insulation and double-layer inflated film. The heat transfer coefficient of the PS pellet insulation is considered at 4.0 W/m 2 ·K for the daytime and 0.3 W/m 2 ·K at night. The overall heat transfer coefficient of a 6-cm thick double-layer inflated plastic film cover is 4.45 W/m 2 ·K, which slightly higher than the value (4.0 W/m 2 ·K) from the ASABE standard [36]. The aging factor may affect the rate of light transmission through the glazing materials; thus, the SOGREEN model allows users to select the degree of aging based on their judgment. The thermal blanket is an important measure to reduce the nighttime heat loss from the greenhouse, so a wide range of thermal properties for the thermal blanket is provided in the model from 3.0 to 0.5 RSI. The ground floor condition and the wetness level can affect the evaporation rate and the indoor thermal environment; therefore, users also need to select floor types, such as soil, mulch, concrete, and wetness level. Based on the plant condition, users need to choose plant density options: very sparse, sparse, ordinary, dense, and very dense. The plant transpiration is estimated based on the plant mass per unit area, which depends on the plant species and density information. Finally, the plant height and distance from the north wall are used to calculate the north wall's shaded area.
The next step is to define the physical and thermal properties of constructional materials for the greenhouse. The dimensions and building materials are set for the north roof, north wall, and floor. As shown in Figures 3 and 4, users input the segment lengths in the north wall and the building material's thermal properties, including density, thermal conductivity, and specific heat. The model also has a built-in material library that facilitates users to find commonly used materials. Figure 4 shows the interface of the greenhouse's detailed physical and thermal properties.   Finally, the operational setting for the greenhouse needs to be defined. It includes th operation hour for the thermal blanket, supplemental lighting schedule, temperature an RH set-points, and ventilation schedule. The model can automatically cover and uncove the thermal blanket based on solar radiation availability. For example, the thermal blanke can be set to unveil in the morning when the outdoor solar radiation reaches 80 W/m 2 an   Finally, the operational setting for the greenhouse needs to be defined. It includes th operation hour for the thermal blanket, supplemental lighting schedule, temperature an RH set-points, and ventilation schedule. The model can automatically cover and uncove the thermal blanket based on solar radiation availability. For example, the thermal blank  Finally, the operational setting for the greenhouse needs to be defined. It includes the operation hour for the thermal blanket, supplemental lighting schedule, temperature and RH set-points, and ventilation schedule. The model can automatically cover and uncover the thermal blanket based on solar radiation availability. For example, the thermal blanket can be set to unveil in the morning when the outdoor solar radiation reaches 80 W/m 2 and cover when it drops below 80 W/m 2 . The user can also define the working schedule for each simulation day.
After completing all settings, the user can start the simulation process, which generally takes 15 to 90 min depending on the selected simulation periods and computer speed. The model can then provide the outputs, including supplemental heating and cooling needs, and the indoor thermal parameters, such as air temperature and RH and the wall and soil temperature.

Model Validation
A commercial solar greenhouse located in Elie, Manitoba (49 • 55 N, 97 • 28 W) was used for validation of the SOGREEN model. The greenhouse has the classic structure of mono-slope CSGs ( Figure 5). Three days of measurement data (28 to 30 March 2017) by Ahamed et al. [6] were obtained to validate the model. The greenhouse is 28 m in length and 6.7 m in width. The north wall and ridge heights are 2.1 m and 3.5 m, respectively, and 34 • is the angle between the north roof and the horizontal plane. The south roof is covered with a 6-mil single-layer polyethylene film, while the cotton thermal blanket (RSI-1.2) covers the south roof from the outside at night. The north wall is made of wooden stud wall; from outside to inside are corrugated galvanized sheet steel (2 mm), fiberglass insulation (152 mm), plywood (13 mm), sand (152 mm), and corrugated galvanized steel (2 mm). A portion of the north wall interior surface was painted black to absorb solar energy. The north roof is made of corrugated galvanized sheet steel (2 mm), fiberglass insulation (152 mm), plywood (13 mm), and plastic film from inside [6]. Table 1 lists the thermal properties of the materials for the north wall, sidewall, and north roof obtained from the ASHRAE standards [35]. needs, and the indoor thermal parameters, such as air temperature and RH and the wal and soil temperature.

Model Validation
A commercial solar greenhouse located in Elie, Manitoba (49°55′ N, 97°28′ W) was used for validation of the SOGREEN model. The greenhouse has the classic structure o mono-slope CSGs ( Figure 5). Three days of measurement data (28 to 30 March 2017) by Ahamed et al. [6] were obtained to validate the model. The greenhouse is 28 m in length and 6.7 m in width. The north wall and ridge heights are 2.1 m and 3.5 m, respectively and 34° is the angle between the north roof and the horizontal plane. The south roof is covered with a 6-mil single-layer polyethylene film, while the cotton thermal blanket (RSI 1.2) covers the south roof from the outside at night. The north wall is made of wooden stud wall; from outside to inside are corrugated galvanized sheet steel (2 mm), fiberglass insulation (152 mm), plywood (13 mm), sand (152 mm), and corrugated galvanized stee (2 mm). A portion of the north wall interior surface was painted black to absorb solar energy. The north roof is made of corrugated galvanized sheet steel (2 mm), fiberglass insulation (152 mm), plywood (13 mm), and plastic film from inside [6]. Table 1 lists the thermal properties of the materials for the north wall, sidewall, and north roof obtained from the ASHRAE standards [35].    The height of the newly transplanted tomato plants was about 14 cm during the experiment. The distance between tomato plants was about 31 cm, and the space between the north wall and the bed was 96 cm. The outdoor temperature ranged from −2.0 • C at night and 10.0 • C at noon ( Figure 6). An electrical heater (3.6 kW) controlled by a thermostat was used to heat the greenhouse when the indoor temperature dropped below 12 • C, and the heater turned off when the temperature reached 18 • C. The cotton thermal blanket was rolled down to cover the south roof before the sunset at 5:30 p.m. and rolled up to uncover the roof after the sunrise at around 7:00 a.m. The vent was opened manually to reduce the indoor air temperature at noon when the indoor temperature was very high. For validation, the air exchange by infiltration (0.156 m 3 /s) was considered most of the time (2:30 p.m. to 11:00 a.m.) because no intentional ventilation was allowed to the greenhouse. The vent was typically opened between 11:00 a.m. to 2:00 p.m. and the air exchange by ventilation was estimated at 0.52 m 3 /s. A detailed description of the experimental setup can be found in Ahamed et al. [6].  (Figure 6). An electrical heater (3.6 kW) controlled by a therm stat was used to heat the greenhouse when the indoor temperature dropped below 12 ° and the heater turned off when the temperature reached 18 °C. The cotton thermal blank was rolled down to cover the south roof before the sunset at 5:30 p.m. and rolled up uncover the roof after the sunrise at around 7:00 a.m. The vent was opened manually reduce the indoor air temperature at noon when the indoor temperature was very hig For validation, the air exchange by infiltration (0.156 m 3 /s) was considered most of t time (2:30 p.m. to 11:00 a.m.) because no intentional ventilation was allowed to the gree house. The vent was typically opened between 11:00 a.m. to 2:00 p.m. and the air exchan by ventilation was estimated at 0.52 m 3 /s. A detailed description of the experimental setu can be found in Ahamed et al. [6].  Figure 7 shows the comparisons of the predicted and measured indoor air temper ture in the greenhouse. The predicted temperature closely followed the measured valu with 1.8 °C of average discrepancy and a maximum difference of about 8.8 °C. Large d crepancies often occurred at noon; the vent's opening for cooling caused the sharp mea ured temperature drops at noon. Figure 7 also shows that the predicted temperature i creased sharply at 8:00 a.m. on the first day, while the measured temperature increas relatively slowly, which could be due to the unwanted ventilation (not considered in sim  measured temperature drops at noon. Figure 7 also shows that the predicted temperature increased sharply at 8:00 a.m. on the first day, while the measured temperature increased relatively slowly, which could be due to the unwanted ventilation (not considered in simulation) caused by the greenhouse entrance door's frequent openings.  Figure 8 shows the comparison of the measured and predicted temperatures for north wall surface. In general, the diurnal profiles have a similar trend, but the predic values are higher than measured ones with an average discrepancy of 4.2 °C and the hi est difference of 9.7 °C. The discrepancy could mainly be caused by possibly large discr ancies of the actual values of the thermal properties of the wall materials (sheet steel, sa (wetness), wood stud, etc.) with the book values selected for the model. Furthermore, model is limited in defining the sheet metal's corrugated shape (larger surface area), s uses a flat surface instead. With some modifications of the thermal properties, the mo predictions could be improved, although this study did not do so in order to stick to original book values. Similarly, the overall trend of the predicted indoor RH is close to the measured one except during the noon ventilation periods; the average discrepancy is about 7.0%. The high discrepancy could be caused due to two factors. Firstly, actual plant transpiration was very small as the plants were transplanted a few days before the experiment. The evaporation from the wet soil mainly dominated the moisture production at noon. Secondly, the air exchange rate during the ventilation period was based on assumptions. This study used an air exchange rate based on constant input parameters, which might differ from its actual value. Figure 8 shows the comparison of the measured and predicted temperatures for the north wall surface. In general, the diurnal profiles have a similar trend, but the predicted values are higher than measured ones with an average discrepancy of 4.2 • C and the highest difference of 9.7 • C. The discrepancy could mainly be caused by possibly large discrepancies of the actual values of the thermal properties of the wall materials (sheet steel, sand (wetness), wood stud, etc.) with the book values selected for the model. Furthermore, the model is limited in defining the sheet metal's corrugated shape (larger surface area), so it uses a flat surface instead. With some modifications of the thermal properties, the model predictions could be improved, although this study did not do so in order to stick to the original book values. Figure 9 shows that the predicted soil surface temperature typically followed a similar pattern with higher daytime predictions than measured values, while at night, the two are very close except when the electric resistance cable heater was in operation for the third night, which the model did not consider. The average discrepancy between predictions and measured values is 2.3 • C, and the maximum is 7.9 • C. ancies of the actual values of the thermal properties of the wall materials (sheet steel, sand (wetness), wood stud, etc.) with the book values selected for the model. Furthermore, the model is limited in defining the sheet metal's corrugated shape (larger surface area), so it uses a flat surface instead. With some modifications of the thermal properties, the model predictions could be improved, although this study did not do so in order to stick to the original book values.  Figure 9 shows that the predicted soil surface temperature typically followed a similar pattern with higher daytime predictions than measured values, while at night, the two are very close except when the electric resistance cable heater was in operation for the third night, which the model did not consider. The average discrepancy between predictions and measured values is 2.3 °C, and the maximum is 7.9 °C.  Table 2 lists the statistical parameters, including the coefficient of determination (R 2 ), standard deviations (SD), mean absolute error (MAE), root mean square error (RMSE), and relative root means square error (rRMSE) for the model validation [6,37]. The predicted air, wall, and floor temperatures look satisfactory, with R 2 values 0.79-0.86, but are relatively low for RH. The SD and MAE value is also high for RH and less than 2.30 °C for temperature except the MAE for the north wall. Compared with other similar mechanistic dynamic models, SOGREEN has good accuracy; the RMSE of the room air temperature for a conventional greenhouse is 5.67 °C [32], 5.3 °C for a semi-solar greenhouse [38], 2.82 °C for a passive solar greenhouse [39], 2.6 °C for CSGs [14], and 1.46 °C (RMSE) and 0.89 °C (MAE) for black-box models [16,28]. For RH, the RMSE of previous mechanistic models is ranged between 4.3-14.6% [16,32], and is 2.5% for the black-box model [16]. Compared with previous studies, the SOGREEN model also has good accuracy for predicting the soil surface temperature but is less accurate for the north wall. For soil temperature, an RMSE of 3.45 °C was reported for a semi-solar greenhouse in Mohammadi et al. [38] and 2.19 °C in Taki et al. [40], but these studies were conducted in a small fully-controlled greenhouse,  Table 2 lists the statistical parameters, including the coefficient of determination (R 2 ), standard deviations (SD), mean absolute error (MAE), root mean square error (RMSE), and relative root means square error (rRMSE) for the model validation [6,37]. The predicted air, wall, and floor temperatures look satisfactory, with R 2 values 0.79-0.86, but are relatively low for RH. The SD and MAE value is also high for RH and less than 2.30 • C for temperature except the MAE for the north wall. Compared with other similar mechanistic dynamic models, SOGREEN has good accuracy; the RMSE of the room air temperature for a conventional greenhouse is 5.67 • C [32], 5.3 • C for a semi-solar greenhouse [38], 2.82 • C for a passive solar greenhouse [39], 2.6 • C for CSGs [14], and 1.46 • C (RMSE) and 0.89 • C (MAE) for black-box models [16,28]. For RH, the RMSE of previous mechanistic models is ranged between 4.3-14.6% [16,32], and is 2.5% for the black-box model [16]. Compared with previous studies, the SOGREEN model also has good accuracy for predicting the soil surface temperature but is less accurate for the north wall. For soil temperature, an  [40], but these studies were conducted in a small fully-controlled greenhouse, whereas SOGREEN was validated against data from a commercial greenhouse with multiple uncontrolled factors (frequent door opening, manual control of thermal blanket, and water tanks placed inside the greenhouse). In previous studies, the RMSE of the north wall was reported as 2.0 • C in Mobtaker et al. [39] and 1.8 • C in Ahamed et al. [6], but it is relatively higher (4.68 • C) for SOGREEN. It needs to be noted that the north wall is the most complicated component to model in CSGs, as many factors affect its temperature variation. Previous studies [30,41] also indicated that a rRMSE value of around 10% is reasonably acceptable for hourly simulation. In general, the results suggest that the model performs very well to predict indoor air temperature but needs to address the high errors for simulating the surface temperatures of the north wall and floor in future studies. Additionally, the limitations of the experimental greenhouses noted above need to be overcome in future studies to obtain accurate test data for further model validation and improvement. The actual thermal properties of the materials should be measured and used in the model instead of the book values, especially ground soil wetness, wall sand density, and moisture content, which greatly impact heat transfer. It also needs to be noted that the model prediction would be much closer to the measured values if the CSGs had an automated heating and ventilation system to control temperature and RH. The manual ventilation and uneven heating could cause unpredictable variations of the indoor thermal environment. Additionally, evapotranspiration is a dynamic process that needs to be addressed in future studies for more accurate results, as the evapotranspiration coefficient is defined based on user input for plant density.

Case Study Greenhouse
The SOGREEN model was used to simulate the annual thermal performance of a conceptually designed CSGs located in Saskatoon, Canada (52.13 • N, 106.62 • W) to predict the heating requirement. The greenhouse is 100 m × 12 m and 5.62 m high in the ridge ( Figure 10). Similar structural materials and dimensions as the greenhouse used in validation are considered except for wall materials (the insulation fiberglass: 218 mm; interior plywood: 19 mm; and heat storage material sand: 399 mm). A large growing space and thicker walls are considered to be able to produce on a commercial scale, increase heat storage capacity, and reduce heat loss. The angle between the south roof and the horizontal plane is set at 40 • to minimize the shading from the south roof. The perimeter insulation consisting of a fiberglass board and plywood is considered beneath the walls and the south end of the roof to reduce the heat loss through the ground. The south roof is considered to be covered with a double-layer inflated film. The indoor ground is covered with landscaping fabric, making a better working place for greenhouse growers. Figure 10 shows the cross-section of the conceptual CSGs. storage capacity, and reduce heat loss. The angle between the south roof and the horizontal plane is set at 40° to minimize the shading from the south roof. The perimeter insulation consisting of a fiberglass board and plywood is considered beneath the walls and the south end of the roof to reduce the heat loss through the ground. The south roof is considered to be covered with a double-layer inflated film. The indoor ground is covered with landscaping fabric, making a better working place for greenhouse growers. Figure 10 shows the cross-section of the conceptual CSGs.

Figure 10. Cross-section of a conceptual CSG in Saskatoon.
A different schedule for the thermal blanket and ventilation rate is considered based on sunrise and sunset times, weather conditions, and likely vent opening for temperature control for each month. No interior thermal screen is considered in the simulation. The greenhouse is equipped with a heating and ventilation system to control the air temperature and RH. The daytime set-point temperature should be around 22 °C for optimal production of tomatoes; however, the set-point temperature is set at 18 °C for daytime and nighttime for two reasons. Firstly, the daytime temperature in CSGs is most likely higher A different schedule for the thermal blanket and ventilation rate is considered based on sunrise and sunset times, weather conditions, and likely vent opening for temperature control for each month. No interior thermal screen is considered in the simulation. The greenhouse is equipped with a heating and ventilation system to control the air temperature and RH. The daytime set-point temperature should be around 22 • C for optimal production of tomatoes; however, the set-point temperature is set at 18 • C for daytime and nighttime for two reasons. Firstly, the daytime temperature in CSGs is most likely higher than 22 • C (except for extremely low outdoor temperatures) when solar radiation is available. Secondly, a lower set-point temperature will reduce the heating cost. During the cold months, a low air exchange rate based on infiltration is set at night and in the morning to reduce CO 2 loss through ventilation, and moderate ventilation rates are arranged at noon for mild months. High ventilation rates with a long ventilation duration are applied during the warmer months. A sunshade screen is considered to block half of the total solar irradiance from June to August when it is needed. Table 3 shows the work schedules in the study greenhouse.

Annual Thermal Simulation
The hourly thermal environment and heating demand in the study greenhouse were simulated for a year, and Figure 11 shows the monthly average heating requirement, indoor temperature, and RH in 2017; the monthly average ambient temperature was below 0°C from November to March (lowest −15.6 • C in January). The average temperature peak was 18.8°C in July. The simulated results indicate that the heating demand fluctuates with the weather conditions, with the highest daily heating load of 7546 MJ in December and 4093 MJ in March. The heating demand is low in April, September, and October with an above-zero average temperature, while no supplemental heating is needed from May to August, although the daily low temperature often fell below 10 • C, showing the benefit of the heat storage capacity of the solar greenhouse.
gies 2021, 14, x FOR PEER REVIEW 14 of Most traditional greenhouses in the Canadian Prairies start operation in March, comparing CSGs and conventional greenhouses starting from March is more appropria As shown in Figure 13, the daily average ambient temperature fluctuated between −21 and 2 °C in March. The average daily total solar irradiance almost quadrupled that December so that the heating load could be reduced significantly.   Three months (December, March, and July) were selected to analyze the daily thermal performance of CSGs in the cold, mild, and warm seasons in Saskatoon. As shown in Figure 12, the daily average ambient temperature fluctuated between −30 • C and 0 • C in December, while the indoor temperature and RH are set at 18 • C and 90%, respectively. On 5 December, the simulated heating load was about 13,000 MJ when the daily total solar irradiance was only 135 W/m 2 , while it was below 6500 MJ on 9 and 10 December with solar irradiance of 1145 W/m 2 . As the sunshine duration is very short in the coldest months (January and December) at the high northern latitudes, the north wall is insufficient to provide heating as a thermal battery, resulting in high heating demand.
Most traditional greenhouses in the Canadian Prairies start operation in March, so comparing CSGs and conventional greenhouses starting from March is more appropriate. As shown in Figure 13, the daily average ambient temperature fluctuated between −21 • C and 2 • C in March. The average daily total solar irradiance almost quadrupled that of December so that the heating load could be reduced significantly.  In July, as shown in Figure 14, the average daily indoor temperature ranged between 22 to 28 °C, and RH fluctuated in an extensive range due to the air exchange rate changing from infiltration at night to high ventilation rate during the daytime. The daily total solar irradiance was high, and a sun blocker is considered to protect the tomato plants. Supplemental heating is not required except for the early morning on 25 July when the ambient temperature is below 10 °C , and the thermal blanket is rolled up.   In July, as shown in Figure 14, the average daily indoor temperature ranged between 22 to 28 • C, and RH fluctuated in an extensive range due to the air exchange rate changing from infiltration at night to high ventilation rate during the daytime. The daily total solar irradiance was high, and a sun blocker is considered to protect the tomato plants. Supplemental heating is not required except for the early morning on 25 July when the ambient temperature is below 10 • C, and the thermal blanket is rolled up.

Heating Cost Analysis
Based on the annual simulation results, the annual heating cost of the solar greenhouse was calculated. This study selected electricity, natural gas, and coal as the heating fuels, and the corresponding heating costs were compared. The cost was estimated as described below: ✓ Electricity: The heating cost using electricity was estimated based on the electrical rate from the City of Saskatoon, which is 14.52 ¢/kWh for the first 14,500 kWh and 7.67 ¢/ kWh after that. ✓ Natural gas: The cost for using natural gas was estimated based on the standard heating value (0.0373 GJ) per unit volume (1 m 3 ) of natural gas [42]. The natural gas burner efficiency is considered to be 92%. The commercial rate of natural gas from SaskEnergy is $38.5 for the basic monthly charge, and the delivery charge is $0.0743/m 3 .

Heating Cost Analysis
Based on the annual simulation results, the annual heating cost of the solar greenhouse was calculated. This study selected electricity, natural gas, and coal as the heating fuels, and the corresponding heating costs were compared. The cost was estimated as described below: Electricity: The heating cost using electricity was estimated based on the electrical rate from the City of Saskatoon, which is 14.52 ¢/kWh for the first 14,500 kWh and 7.67 ¢/kWh after that. Natural gas: The cost for using natural gas was estimated based on the standard heating value (0.0373 GJ) per unit volume (1 m 3 ) of natural gas [42]. The natural gas burner efficiency is considered to be 92%. The commercial rate of natural gas from SaskEnergy is $38.5 for the basic monthly charge, and the delivery charge is $0.0743/m 3 . Coal: The heating value is considered 18 GJ per unit tone of coal for a coal-fired heating system. We assumed the coal price is $45 per ton and a high-efficiency coal boiler with 90% efficiency. This study neglects the cost for residual ash disposal (2.8-6.6 tons). Table 4 provides a comparison of the heating cost of different energy sources. The results indicate that electricity is the most expensive heating source while natural gas and coal have a comparable annual cost, one-tenth of the cost of using electricity. Natural gas has some unique advantages compared to coal, such as low capital costs and a better thermal control system. In addition, the natural gas combustion process does not produce solid by-products, such as ash, which needs additional cost for disposal. Finally, the heating cost of the conceptually designed CSG was compared with a traditional multi-span commercial greenhouse located near Saskatoon, which is heated by natural gas boilers. This greenhouse was closed during the coldest months (December and January), and the heating cost was compared for the remaining ten months (February to November), which is also a limitation for this study for annual evaluation. The heating cost in Table 4 for the conceptual CSG and the prorated natural gas bill for heating Grandora Gardens are presented in Table 5. The solar greenhouse has a much lower energy consumption and achieves 55% of cost-saving. The preliminary results indicate that CSGs could be an energy-saving solution for winter vegetable production in remote northern communities of Canadian Prairies. Therefore, the policymaker or stakeholders need to fund further research and development of this technology for the extreme cold regions and provide financial support for dissemination in the northern communities. Table 5. Heating cost comparison between Grandora Gardens and the conceptual solar greenhouse.

Conclusions
In this study, an existing CSG simulation model (RGWSRHJ) was modified into a new model entitled SOGREEN, which is aimed to predict the heating requirement of CSGs. The new functions of SOGREEN model allow the prediction of the hourly thermal environment of CSGs over the year. Additionally, the modified model allows the temperature and RH control and many different energy-saving technologies, such as insulation, indoor thermal blanket and screen, and additional functions required in modern greenhouses. The model was validated with field data measured in a solar greenhouse in Manitoba, Canada. The average discrepancies between the measurement and prediction are 1.9 • C, 7.0%, 4.2 • C, and 2.3 • C for the indoor temperature, RH, north wall surface temperature, and soil surface temperature, respectively. The model predictions could be improved by using measured thermal properties of the wall and ground materials instead of book values. Finally, a case study was conducted for a conceptually designed CSG (100 m × 12 m) in Saskatoon, Canada, to produce tomatoes. The annual simulation indicates that the daily average heating in the coldest month (January) could be two times higher (6.3 MJ/m 2 ·day) compared with March (3.4 MJ/m 2 ·day). Low supplemental heating is required to grow tomatoes in April, September, and October, when the average daily outdoor temperature is between 3.8 • C to 10.5 • C, and no supplemental heating is needed from May to August. Comparing the study of CSGs with a traditional local greenhouse, the heating cost of CSGs is about 55% less than the even-span gable roof greenhouse. Hence, this study concluded that a CSG has the potential for energy-efficient year-round vegetable production for cold regions, such as the Canadian Prairies, to ensure the food security of these remote communities.
Finally, it could be concluded that the SOGREEN model can predict the environment parameters (temperature and RH) and the heating and cooling loads of CSGs with reasonable accuracy, but the model needs to be improved further to minimize the error in predictions, especially for the north wall. The model was validated using three days of data at the end of winter, so further validation could be accomplished against the data from the other seasons. The limitations of the previous experiment (uncontrolled factors in commercial CSGs) also need to be addressed in future studies. In addition, the case study used the monthly gas bill to estimate the heating cost for the conventional greenhouses; the energy-saving comparison with conventional greenhouses needs to be further studied using more accurate short-term data, such as transient heating data.