## 5 Conclusions  
In this study, we sought to identify the best sampling strategy for indirect measurement of gas volume flow in NVBs.  
* It was found that in stable cross-flow conditions based on the high correlation coefficient between inflow wind speed and the direct method (0.88, vs. 0.81-0.87 for indirect methods) can become a reference method.  
* However, further ways of quality improvement of obtained values via direct method should be found and tested. It has to be noticed that the non-optimal positing of USA devices and availability of wind break nets on the side walls could introduce uncertainty. This can further cause the resulted volume flow reduction.
* Wind-related sample method 1 estimates in stable cross-inflow conditions are closer to the reference method.
* With sample method 2, lower emission values were measured than with sample method 1. This is likely due to an underestimation of inside gas concentrations with method 2, which also takes into account sampling lines positioned toward the inlet of the barn. These contain lower concentrations than the fully accumulated concentrations at the outlet sample line that was chosen for method 1.
* It was found that Tukey transformation can be a valuable alternative to the logarithmic transformation while analyzing very skewed data.  
The obtained results showed that the topic of accurate measurement of volume flow in NVBs using indirect methods should be further investigated. Of course, volume flow deviates between seasons, wind speed, wind direction and other ambient conditions in the barn. Currently, the results presented in this manuscript were obtained in stable cross-inflow conditions with the prevailing southern wind (90\({}^{\circ}\) angle). However, it is not always possible to obtain stable cross-inflow conditions. Thus, further investigations on creation a universal sampling strategy, working within all possible conditions in NVBs should be carried out. This will be the focus of future research, where we plan to integrate a setup with a higher sensor density, which will take into account every opening of the barn as a potential inlet or outlet.  
Conceptualization, D.J. and T.A.; Data curation, D.W. and A.R.; Formal analysis, C.A., E.-H.M.D., B.A. and S.H.; Investigation, D.J.; Methodology, D.J., D.W., E.-H.M.D., T.A. and S.H.; Validation, C.A. and S.H.; Visualization, D.W.; Writing--original draft, D.J., D.W. and S.H.; Writing--review & editing, E.-H.M.D., A.R., B.A. and T.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding. Data Availability Statement: Data are available by the authors upon request.  
We would like to acknowledge [PERSON] and [PERSON], technicians at ATB, for technical support during the measurements, as well as administration of [PERSON] and [PERSON] from State Research Center of Agriculture and Fisheries Mecklenburg-Vorpommern (LFA) for providing data.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
A Area of the opening in the side wall, [m\({}^{2}\)]  
AER Air exchange rate, [h\({}^{-1}\)]  
C\({}_{prod}\) Estimated CO\({}_{2}\) production rate per animal, [g h\({}^{-1}\)]  
CIGR Commission Internationale du Genie Rural  
CO\({}_{2 int}\) Inside concentrations of CO\({}_{2}\), [g m\({}^{-3}\)]  
CO\({}_{2 out}\) Outside concentrations of CO\({}_{2}\), [g m\({}^{-3}\)]  
FTIR Fourier transform infrared  
n Number of partial areas in the barn  
NVB Naturally ventilated barns  
PTFE Polytetrafluoroethylene