RFs selection was based on a review of existing farms in schools and their compatibility with Quito’s educational program. For simulation, lettuce mono-crops  were used because of their compatibility with Quito’s climate. Table 2 depicts the crops relevant characteristics. Following this there is a brief description of the three RF system assessed, and Appendix B contains complete specifications.For the archetype schools in existing conditions, their simulation models were manually calibrated and validated against data measured on-site. Fifteen-minute temperature readings were taken for several classrooms in each school from April to June 2019. Simultaneously, weather data was collected from the nearest meteorological station. Precise simulation weather files were developed to reflect the existing boundary conditions for schools during monitoring. Additionally, sensitivity and uncertainty analyses were conducted for six dynamic or non-measured building parameters: occupancy density, infiltration rate, metabolic rate, natural ventilation setpoint, heating setpoint, and local shading operation. These analyses were incorporated into the stepwise calibration for the baseline models following ASHRAE 14 guideline. However, as calibration was done against indoor air temperature, the thresholds for the normalized Mean Bias Error  and the Coefficient of Variance of Root Mean Square Error  were more stringent than those set in ASHRAE 14. For archetype A, the model has an nMBE of 0.52% and a cvRMSE of 6.42%. For archetype B, the errors are 0.81% and 5.06%, respectively. The average prediction error for both school models is below ±0.6 ◦C. A full description of the calibration and validation of the baseline models is in Ref..

Two different simulation strategies for OAF and pRF are required because the EcoRoof module already incorporates all relevant heat fluxes for soil farms but for pRFs these fluxes had to be incorporated anew. EcoRoof is a one-dimensional green roof model including evapotranspiration, soil’s heat conduction, and convective and radiative heat exchanges between the plants’ canopy and its surrounding air. EcoRoof allows setting parameters related to soil, irrigation and plant type. The crop’s LAI and height are constant throughout the simulation period, which is inappropriate for crops. Authors devised a work around to include crop’s growth in the simulation by using a batch to loop through multiple E+ simulation files. In these files, the crop’s growth sub-model assigned the LAI, height, and cultivar cycle. For hydroponic gutter farms, co-simulation solves crops models in MATLAB and host-buildings in E+. In co-simulation, two subsystems – which form a coupled problem – are modelled independently and simulated in a distributed manner. In this way, the outputs of one subsystem become the inputs of the other. Co-simulation was favoured over E+ scripting because of MATLAB’s ability to create and use complex mathematical functions, debug them without difficulty, and evaluate their behaviour at each iteration. Energy Plus Co-Simulation Toolbox was used to communicate MATLAB and E+. This toolbox was used succesfully for building calibration, occupancy distribution and HVAC predictive controls. This toolbox configures an external interface that acts as a Building Control Virtual Test Bed through which E+ Ptolemy II sends and receives data packages at each time step. E+ engine is called from MATLAB’s interface, and the communication starts at the first simulation time step.Fig. 5 shows the information flow exchange between both software. For each pRF zone, MATLAB sends to E+ three inputs from crops: latent heat [W], sensible heat [W], and CO2 volumetric sink rate.

These inputs were configured in E+ using the Energy Management System  and its “external interface actuator and schedule” objects. Crops were included in the E+ idf files using the “other equipment” and “zone contaminant source and sink: carbon dioxide” objects. For latent and sensible heat fluxes, these “other equipment” objects are configured to have a latent and radiative heat fraction of 1, respectively.Although recently there have been agriculture campaigns in Quito’s schools focused on creating ground farms, these initiatives have been restricted to rural and peri-urban areas. Currently, there are no urban schools that have rooftop farms. This study selected as host-buildings previously validated real “archetype” schools thus enabling researchers to extrapolate building-level results to a city scale. Therefore, the obtained results are a first theoretical assessment for the adequacy of RFs for this uninsulated free-running building stock. In this section, firstly, there is an assessment of how crops affect indoor environments and the proof of concept of the proposed sub-models. Secondly, the RFs theoretical performance for Quito’s archetype schools is discussed regarding heat flux, IEQ and EUI. Thirdly, there is a general discussion on the benefits and setbacks of these simulation strategies.Similar results were obtained for both schools. Plants emit heat during the night due to the release of stored radiation. However, the most significant heat exchange occurs during the daytime due to transpiration. This heat exchange causes the greenhouse air thermal amplitude to decrease. For RTGs in Quito, crops lower daytime air temperature on average 0.75 ◦C and raise the night-time temperature by 0.45 ◦C. This effect is more significant in peak temperatures with nominal values of − 1.8 ◦C and +1.3 ◦C at noon and midnight, respectively. Similar temperature differences were reported for simulated planted and unplanted RTGs in London.

LAI is one of the most influential parameters on a crop’s energy balance since higher LAIs reduce cooling loads more efficiently. Fig. F.1 in Appendix F shows the effect of LAI in classrooms’ heating demand and indoor air temperature for a typical school week. Crop’s growth is more influential in eGRs as simulation showed that a 1-unit increment in LAI changes the heating load by 18.11 Wh/m2 and -2.28 Wh/m2 for eGRs and RTGs, respectively. Though the crop’s sub-models used in this co-simulation have been validated extensively in the literature, it is not appropriate to consider the predictive capability of this model as fully validated. The lack of empirical rooftop farm data for calibration and validation of this co-simulation is a limitation in this study. As proof of concept, Table 5 shows a comparison of experimental data on hydroponic lettuce cultivated under greenhouse conditions found in the literature and the outputs obtained in this research. It is worth remarking that, for this comparison, the co-simulation outputs correspond to the cultivar cycle described above. Additionally, to match the experimental conditions reported in the literature, a ±50 W/m2 range was used for solar radiation and a ±0.25 range for LAI. Co-simulation outputs are close to experimental thresholds reported in the literature therefore showing the adequacy of the proposed simulation. Though experimental validation in Quito could not be conducted for lack of real experiment sites, these first results provide a high level of confidence regarding the impact of crops on these buildings.Both archetype schools have similar thermal balances but the roofs show a significant difference. Roofing in archetype A contributes a heat gain of 1804.56 kWh/year, and in Archetype B, a heat loss of 7980.68 kWh/year. Simulation models showed roofs receive twice as much radiation as walls.

Considering the high daily horizontal radiation in Quito,RFs provided a significant change in the roof’s heat transfer rate. eGRs reduce heat flow more effectively due to the increment in thermal mass and insulation – 50% daily reduction for archetype A and 85% for archetype B, with similar results reported in the literature. However, RTGs and iRTGs have higher heat gains with an average of 33.7 kWh/m2 in archetype A and 47.16 kWh/m2 in archetype B. These higher heat gains are in line with values reported in the literature. RTGs’ heat gains invert the stratification between external and internal roof surfaces. External surfaces  are warmer than internal  on average 2.27 ◦C for archetype A, and 1.0 ◦C for archetype B. eGRs have temperature gradients below 0.41 ◦C but with the internal surface being warmer than the external. During sunlight hours, eGRs lower the average daily maximum external surface temperature by 3.71 ◦C and 8.42 ◦C for archetype A and B, respectively; and reduce the average surface temperature by 2.4% and 15.87%. These values are lower than surface temperature reductions reported in the literature, with an average summer daily reduction of 20% for sedum GRs in Italy and a 30% reduction in France. Those studies focus on summer conditions when foliage shading and evapotranspiration are higher. However, those studies also suggest lesser effects for sunny winter conditions more comparable to the climate used in this article. Fig. 7 shows the average hourly heat flux and surfaces temperature difference for the studied RFs. Roof slabs establish the hourly flux flow direction due to their thermal inertia. The low inertia of the 6 mm cement sheet roofing in school A  results in the heat flux directly proportional to the roof’s surface temperature difference. In contrast, the high thermal inertia of the concrete slab in school B and the new 10 cm composite deck in school A cause a 6 to 8 hours lag between the maximum surface temperature and the maximum heat flux transmitted to the interior space.

This lag is a known quality of high thermal mass constructions. eGRs slow heat transmission through the roof and release it during the first morning hours. RTGs and iRTGs have heat flux patterns similar to those of their slabs but with a surplus of heat gains due to the shelter space created. This daily heat surplus is increased slightly  due to the exchange of air and CO2 between greenhouses and classrooms, hydroponic nft channel especially at night.In baseline scenarios, during occupancy hours, Top reaches low values of 12.74 ◦C and 13.02 ◦C, for school A and school B, respectively. The average daily temperature falls at 18.87 ◦C but reaches hourly maximums of 27.5 ◦C and 24.7 ◦C in school A and B, respectively, because of roofing materials. All RFs scenarios increase classrooms minimum operative temperature with RTG achieving the most considerable difference,followed by eGR,and lastly iRTG  because airflow integration removes heat from the classrooms. By acting as passive heating systems, RTGs increase Top significantly but do not attenuate temperature gradient, i.e. RTGs provide an offset temperature to current roofs. For Quito, this offset is beneficial as it raises temperatures to a maximum of 25.8 ◦C, within thermal comfort conditions. Fig. 8 displays the hourly indoor air temperature in classrooms for all assessed scenarios during peak cold and warm days. eGRs insulation effect reduces indoor temperature fluctuations, especially on warmer days, but without the detrimental effects shown for mild cold conditions in previous studies. During occupancy periods, archetype schools currently only meet thermal comfort conditions – 19.6 to 26.6 ◦C – from 11 a.m. onwards, evidencing sub-optimal conditions as previously detected from students thermal perceptions surveys.

Temperatures below comfort occur for 34.4% and 48% of occupancy hours for archetypes A and B, respectively. However, both schools have similar DDH due to the high thermal amplitude in school A. Table 7 summarizes the improvement in thermal comfort due to the thermal coupling of RFs in school buildings. All assessed RFs increase comfort due to farms’ insulation effect, boundary condition change, and flux exchange. For school A, the three RFs diminish classrooms’ DDH but do not significantly improve the hours in thermal comfort, whereas in school B, all RFs achieve significant results. This difference occurs because school A existing roofing – low thermal mass and albedo – heats the classrooms quickly during the early morning hours, thus improving comfort. Nevertheless, as solar radiation increases, the existing roofing causes overheating and high-temperature gradients. Simulation results showed that natural ventilation alone is not enough to control this overheating, and thus mechanical cooling is needed. For both schools, iRTGs have higher DDH than RTGs because classrooms act as the primary heat source, therefore losing heat through forced ventilation. However, this integration is favourable for farms since it increases air temperature by 0.11 ◦C and decreases hours below comfort conditions by 2.1% – considering a 14 to 18 ◦C thermal comfort range for lettuce. iRTGs integration main benefit is the displacement of CO2 from classrooms to greenhouses to serve as a natural fertilizer. During occupancy, classrooms have CO2 peak levels of 3725.2 ppm. The literature cites CO2 concentrations between 2000 and 3000 ppm for classrooms with 25 students, a density lower than in Quito. The recommended maximum CO2 concentration according to EN-16798-1 for Category 2 buildings is 500 ppm above external levels. Currently, classrooms exceed this limit during 26.2% occupancy hours, but integration could lower this by 10.5%.