## 1 _Article_
In turn, these vortices can bring gases from inside to the exterior, and if the outside sample sensors are installed too close to the barn, the data used to find differences between interior and exterior concentrations will be incorrect. Recommendations on measurement approaches are given in the VERA protocol [16]. However, these recommendations also require several individual adaptations for each specific barn, geographic region, and set of weather and wind conditions. In this study, in order to measure the volume flow in NVB, we employ two approaches: a direct and an indirect method. The direct method is a fundamental approach that requires estimation of the airflow at the inlet of the barn [17]. Calculating volume flow via the direct method is relatively simple; the wind velocity at the openings is multiplied by the area of the opening at the building's inlet or outlet [18]. A great advantage of this method is in its simplicity; it does not require information about animal physiology and behavior to estimate the resulting volume flow. However, the method's result is strongly dependent on the precision of the perpendicular air velocity vector because of the fluctuations that occur during the course of measurement [17]. Another requirement is that the inlet must be covered by as many anemometers as possible, which must accurately measure the velocity components (e.g., ultrasonic anemometer). However in constantly changing wind conditions, this is hard to achieve. It can be done, for example, by manually sorting out cases, where the specific stable wind conditions can be reached. Indirect gas balancing methods are the most common alternative to the direct method. These methods use either artificial tracer gases, which are injected into the barn [19; 20], or the natural tracer gas, CO\({}_{2}\), which is produced by the livestock within the barn [14; 17; 21; 22]. In this manuscript, we employ a CO\({}_{2}\) mass balance method using natural CO\({}_{2}\) sources to calculate the volume flow. The method offers several advantages: it can be used without any additional injection systems or additional harmful tracer gases (for example, SF\({}_{6}\); [23]),it is cheap to run, and the CO\({}_{2}\) produced by animals generally mixes well in the barn [9]. However, the CO\({}_{2}\) balance method cannot be used in the absence of animals (for example, outside walking alleys) and neglects the fact that endogenous CO\({}_{2}\) can lead to potential measurement errors. CO\({}_{2}\) balance methods also require correct measurements of the outside and inside concentrations of gases in multiple locations [14]. Combinations of sampling line (points) locations can lead to different sample strategies. As a result, there are different options to quantify the CO\({}_{2}\) gas concentrations. [PERSON] et al. [24] presented a comparison of different sampling strategies created for estimating ventilation rates and ammonia emissions in a naturally ventilated dairy barn in Northern Germany, each of which is appropriate in certain circumstances. They showed that combinations of sampling strategies can lead to different CO\({}_{2}\) concentration measurements, and in consequence, to differences in the estimation of the volume flow of up to 80%, 94%, and 63% for winter, transition and summer periods, respectively. Based on the literature review, the authors suggested the best sampling strategy, but further verification analysis is required. The literature review on measuring emission of gases in NVB and positioning the sampling lines inside and outside the dairy barn showed a lack of a \"golden standard method\", showing which sampling method is the most accurate. [PERSON] et al. [24] assumed that for certain wind conditions, the optimal sampling method exists. Since there was no reference method to compare the sampling methods against, the authors provided an intercomparison between the delivered methods without identifying a superior approach. However, suitable conditions, where each method provides optimal results, were shown.