Model Validation

The validation was based on the model calibration process through the comparison of monitored and simulated data from the living room. Nowadays, this is frequently used in research as a means of validating results by calibrating the model through the comparison of monitored data in short periods of time and building simulations to identify thermal comfort and energy benefits [8,24–26]. Monitored data at various points in the building were used for model calibration (Figure 6). The indoor air temperature of the main room was used as the parameter for model validation, given its strong connection to the thermal environment of the entire building. The simulated temperature in the main room was compared to the values recorded during observation periods (Figure 18). The comparison evaluated indicators used by the scientific community and defined by international organizations such as the American Society of Heating, Refrigerating and Air Conditioning (ASHRAE) and the National Renewable Energy Laboratory (NREL) [27], which establish acceptable ranges for statistical calibration rates. After calibration, hourly and monthly

simulation data for an entire year could be obtained. A model is considered valid if the difference between the simulated and monitored values falls within the acceptable range defined by international standards (RMSE 10% and NBME 25%) [28,29]. Two well-accepted statistical indicators for model validation are the normalized mean bias error (NBME) and the root mean square error of the bias (RMSE). To assess the correlation between the simulation and monitoring results, specific criteria were adopted. These criteria are formally defined as follows:

$$NMBE\left(\frac{0}{0}\right) = \frac{\sum\_{i=1}^{n} \left(t\_{ip} - t\_{mi}\right)}{n - 1} \times \frac{1}{\frac{t\_{m}}{\underline{t\_{m}}}} \times 100$$

$$CV(RMSE)\left(\frac{0}{0}\right) = \sqrt{\frac{\sum\_{i=1}^{n} \left(t\_{ip} - t\_{mi}\right)^{2}}{n - 1}} \times \frac{1}{\frac{t\_{m}}{\underline{t\_{m}}}} \times 100$$

**Figure 18.** Temperature difference between monitored and simulated values in the main room.

In this study, the simulated temperature values (*tip*) of node *i* were compared to the monitored temperature values (*tmi*) of node *i*, where the arithmetic means of a sample of *n* measured temperature data (*tm*) were calculated, and *n* was the number of monitored temperature data during the monitoring period. The normalized mean bias error (NMBE) indicator provided information on the difference between the simulated and measured temperatures. A positive NMBE value indicated that the simulated temperatures were higher than the monitored data, whereas a negative value indicated that the simulated temperatures were lower than the monitored temperatures. The ideal NMBE value was zero.

The coefficient of variation of the root mean square error (CV(RMSE)) indicator quantifies the relative correlation, expressed as a percentage, between the differences (simulated temperatures minus monitored temperatures) and the average of all the monitored temperatures [24,26]. The CV(RMSE) value is always positive, and an ideal value would be zero, indicating optimal accuracy. NMBE values, on the other hand, indicate the presence of systematic error or bias in the simulation. In contrast, CV(RMSE) serves as an indicator of precision, reflecting how closely the simulated results align with the monitored data. The temperature differences between the monitored and simulated temperatures in the main room are presented in Table 5. Additionally, the coefficient of variation of the root mean square error (CV(RMSE)) was calculated, which was 4.46%, and the normalized mean bias

error (NMBE) was found to be 4.28%. Both values were below the maximum validation threshold of 25% recommended by the ASHRAE [28].

**Table 5.** Temperature differences between monitored and simulated data in the main room. NMBE and CV (RMSE) values.


#### *3.3. Assessment of Annual Thermal Performance*

A comprehensive one-year simulation of the building was conducted using the validated model and its corresponding input parameters for annual simulations. In order to examine the dynamic free-running thermal behavior of the living room environment, the impact of free gains was deliberately disregarded.

Figure 19 presents the annual differences in the temperature of the simulated main living room and the outside temperature. It can be observed that the outdoor temperatures are representative of cities located at altitudes between 2000 and 3000 m above sea level in the Andean Mountain region on the Equatorial Line (such as the city of Azogues), which have a cold climate that affects the indoor temperatures of buildings. Regarding the indoor thermal comfort range between 18 ◦C and 22 ◦C, it can be observed that the simulated temperatures are mostly below the range. The number of hours per year that the building is below 18 ◦C is 7.338 h, that below 16 ◦C is 6.207 h, and that below 10 ◦C is 538 h. These values show that the indoor environment of the building, despite having temperatures below the comfort range, never reaches extreme cold temperatures or below 0 ◦C, which is

a characteristic of buildings that do not have active heating systems. This has caused the residents to adapt to lower temperatures and compensate for them with clothing [20].

**Figure 19.** Variations in air temperature of the main room over one year.

Figure 20 presents data on the relative humidity throughout one year at an hourly resolution. The humidity ratio in the main living room ranged from 4 to 11.7 g of water vapor per kilogram of dry air. The upper limit of relative humidity was set at 70%, indicating that the relative humidity values did not exceed this threshold throughout the evaluation period.

**Figure 20.** Variations in relative humidity of the main room over one year.

In Figure 19, the dashed line of simulated temperatures for one year in the living room shows the range obtained, with indoor temperatures ranging from 15 ◦C to 18 ◦C and relative humidity between 2 and 9 g of water vapor per kg of dry air, with an acceptable upper limit of 19 g of water vapor per kg of dry air and maximum acceptable relative humidity of 70%. This indicates that the traditional courtyard houses in the city of Azogues adapt well to the local climatic conditions, primarily due to their thermal masses. Additionally, the higher simulated temperatures in the living room compared to the exterior, even at night, demonstrate that the case study has passive design strategies that improve the indoor temperatures. This temperature value could potentially improve if the U-value of the thermal transmittance of the building's envelope decreases to 2.35, as stipulated by local regulations. In this way, the internal thermal gains would be retained, and more appropriate thermal comfort standards could be achieved.

If we analyze the annual thermal performance of the building with the temperature and relative humidity data from the living room, we can verify that the simulated temperature in the main room exceeds the 16 ◦C recorded during the monitoring period. Additionally, the annual relative humidity of the simulated main room matches the relative humidity recorded in the same space at 70%, allowing the building's occupants to adapt to the indoor environment despite having slightly lower temperatures than those recognized as the comfort range.
