## 2 Materials and Methods
### Estimation of Ventilation Rates
In particular, naturally ventilated rooms can present rapid changes in the ventilation rate, which is highly dependant of environmental variables (e.g., wind speed). Thus, it might be advisable to independently estimate as many parameters as possible. For the CO\({}_{2}\) generation rate this can be difficult. Although there are references for individual generation rates, they depend on the sex, age, weight, height and metabolic activity of the occupants. Furthermore, occupation should be constantly monitored [5; 32]. Additionally, \(C_{\text{ext}}\) is a somewhat cumbersome parameter. If the air entering the space was guaranteed to come from outside, it could be estimated between 350 ppm and 400 ppm. Nonetheless, this is hardly ever the case. Air could be flowing in from other parts of the building, where there could be significant occupation, so part of the air entering the room may have CO\({}_{2}\) concentrations well above atmospheric levels. In this case, \(C_{\text{ext}}\) should be interpreted as a weighted mean of the concentrations at the different points of entry by the respective airflow. It follows that usually \(C_{\text{ext}}\) cannot be measured. As a consequence of the aforementioned problems, Equation (3) has usually been adjusted for simplified situations. For example, it is common to adjust it to CO\({}_{2}\) measurements made just after a room is emptied, when there is no generation, or when equilibrium is achieved [5; 6; 8; 9]. These are usually referred to as the decay and the equilibrium methods, respectively. These simplified methods have the disadvantage of only being able to depict ventilation rates during specific situations. Alternatives like the ones in [5; 7] have been proposed, but they usually require filtering high frequency noise out of measurements, which is not simple, as there could also be high frequency changes in the model's parameters. As an alternative, we present a novel adjustment methodology for the classical box model, which is remarkably simple. It can easily be shown from Equation (2) that the CO\({}_{2}\) equilibrium concentration is  
\[C_{\text{eq}}=C_{\text{ext}}+\frac{nG}{Q} \tag{4}\]  
Using Equation (4) as a change of variable in Equation (3), Equation (5) is obtained. \[C(t)=C_{\text{eq}}-(C_{\text{eq}}-C_{\text{o}})e^{-\frac{Q}{t}} \tag{5}\]  
Equation (5) can be directly fitted to data with several advantages over Equation (3). It reduces the number of explicit parameters in the model, which simplifies the application of regression methods. Furthermore, occupation levels, CO\({}_{2}\) generation rates and \(C_{\text{ext}}\) do not explicitly participate in the model. Instead, they are considered under \(C_{\text{eq}}\), which can be estimated from the CO\({}_{2}\) concentration time series, as it is its horizontal asymptote. Finally, \(C_{\text{o}}\) can easily be obtained by restricting a certain interval around the first point in the adjusted concentration series. A final remark should be made regarding the selection of adjustment intervals. If a continuous CO\({}_{2}\) time series is available, it should be sectioned in several adjustment intervals, which will be referred from now on as adjustment windows. For the present paper, this selection was manually executed via visual inspection of data. Portions of concentration time series with no clear exponential evolution were not fitted. The selection was assessed in terms of the adjustment Root Mean Square Error (RMSE), which was found to be always well below instrumental uncertainty. Future work will pursuit automation of the adjustment windows selection process.