## 4 Discussion  
In this study, we used the direct method as a basis for measuring the quality of indirect estimates of volume flow using two sampling strategies in an effort to identify the best approach. For example, [PERSON] et al. [17] used the direct method as a reference for evaluating common indirect method in determining air exchange rate (AER). In this manuscript, we determined the answers on two questions. The first is, can we use the direct method as a reference method for identifying the best indirect approach under cross-flow conditions? The second is, which sampling method in stable cross-flow conditions produces more accurate outputs in comparison with reference method? We found that the resulted volume flow obtained via the direct method showed high significant correlation with wind speed (0.88); hence, the direct method is an appropriate basis for comparison in this context. However, within the high correlation, there are factors influencing the values obtained via the direct method, which we cannot consider in our calculations, for example, the heights of the installed USA devices (according to the roof) and the distance to the open side of the barn. Such positioning of the USA devices can be the reason for recording a lower air velocity (parameter \(R_{velocity}\) in the Equation (1)) and as a result, the total volume flow can be also reduced. Another important parameter used for calculating volume flow (Equation (1)) is \(A\), which describes the area of the openings in the side wall. It was calculated based on the permeability of the air passing through the wind break nets on the side wall. This implies that the velocity must be measured in the direct area in close proximity to the nets. Since this condition is unfeasible, the resulted volume flow values can also be reduced. Further, we conducted statistical analyses with the aim of identifying the best indirect sampling method out of two relative to the reference (direct) method. We employed two indirect methods based on the CO\({}_{2}\) balancing method. Hence, we assumed that a wind-related strategy can estimate concentration more accurately in stable cross-ventilated conditions. We found a prevailing wind flow (southern) with the angle of 90\({}^{\circ}\) and removed all cases where the wind was not approaching the barn from the southern side (within the spin of the barn, the wind thresholds were 152-242\({}^{\circ}\)). It is clear that seasonality and wind direction fluctuations play a crucial role in identifying the volume flow in NVBs. [PERSON] et al. [24], [PERSON] et al. [28], [PERSON] et al. [38], [PERSON] et al. [39] stated that in the cold period, the volume flow values are generally lower, and in the warm period they are higher. [PERSON] et al. [14] researched the same barn, and it was found that the highest volume flow values were observed within the southern wind directions, whereas the lowest values were observed within eastern flow. Thus, in the current setup, since we measured volume flow in the cold period (September 2017-February 2018), the obtained volume flow values within two indirect and direct methods are lower in comparison with annual distribution. However, according to wind direction, the values are higher since we sorted out the cases only with southern wind. Next, we conducted correlation analysis between volume flow obtained through the direct and the two indirect methods. Wind-related SM1 has lower Pearson correlation coefficients (0.74) than SM2 (0.78). However, the difference between correlation coefficients for SM1 and SM2 is relatively small, and based only on correlation coefficients, it is hard to identify the best method. In general, both indirect methods show a much higher spread of values in comparison with the direct method. [PERSON] et al. [17] reported the same result. They outlined such behavior due to the limitation of the production term considered in the calculations of volume flow.