Verification Analysis of Volume Flow Measured by a Direct Method and by Two Indirect CO₂ Balance Methods

Abstract

Ammonia and greenhouse gases have a negative impact on the environment. The most important agricultural sources of ammonia are dairy cattle housing systems, which are mainly naturally ventilated. Estimating emissions for naturally ventilated barns (NVB) is challenging due to the large number of influencing factors. Most notably, the direct coupling of the inside flow regime with ambient and turbulent weather conditions causes difficulties in measuring ventilation rates, gas concentrations and emissions; thus, different methods are available. In this study, we compared the outputs of total volume flow obtained by two indirect methods (CO${}_2$ mass balance) to the direct method. The latter we assume in this study as the reference method since it is a fundamental approach that estimates airflow on the inlet. In the context of mass balancing, we compared wind related (sampling method 1) and non-wind related (sampling method 2) approaches for measuring CO${}_2$ concentrations. The total volume flow calculations were based on hourly measurements of CO${}_2$ concentrations obtained by Fourier transform infrared (FTIR) spectrometer. Data were collected over a period of six months. The values of the total volume flow were filtered for prevailing southern winds (90${}^{\circ }$ angle). The wind related method (sampling method 1) in stable cross-inflow conditions produces more accurate and realistic values in terms of the general representation of the values in comparison with direct method and can be considered further for measurements of volume flow in the NVBs.

1. Introduction

Agriculture, and in particular, livestock, contributes more than 18% of global greenhouse gases emissions either directly via emissions from enteric fermentation in livestock, urine excretion, microbial activities in manure, etc., or indirectly via emissions from applications on farm crops, production of food for feeding livestock, processing and transportation of livestock products, etc. [1]. Determining the emission factors in livestock buildings requires accurate measurements of gas concentrations and precise calculations of ventilation rates. However, especially in naturally ventilated barns (NVBs), which have large openings and large contact surfaces with the outdoor environment, the estimation of the ventilation rates is complex and involves large uncertainties [2]. The air flow in NVB is mainly influenced by the natural driving forces of wind and thermal buoyancy [3,4,5].

Large openings in NVBs also cause non-homogeneous distributions of gases inside the barn, which makes the positioning of gas measurement setups challenging [6,7]. The optimal positioning of the sampling location to obtain the most reliable measurements of CO${}_2$ and NH${}_3$ concentrations has been widely discussed in the literature [8,9,10,11,12,13].

König et al. [14] performed a sensitivity analysis on the calculation of the air exchange rate by varying the indoor and outdoor sampling points. They found that the optimal sampling location inside the barn depends on the characteristics of approaching wind flow. Thus, it is recommended that more than one sampling point is considered to reduce errors. The authors found that sampling points in the center may provide more accurate estimations of air exchange rates than measurements obtained from the side way points. The location of the outside points must also be carefully considered and placed at a distance where the influence of the interior concentrations will not be significant.

Another work with sampling points was conducted by Van Buggenhout et al. [8]. They used point-wise measurements in the mechanically ventilated room. Van Buggenhout et al. [8] found that even for the room taken in the experiment, the positioning of sampling points can significantly influence the estimations of volume flow and cause measurement differences of up to 86%. As it is stated in [15] the difference (up to 86%) is due to the strong dependence on outside weather conditions, barn geometry, the location of other sources of gaseous emission in close proximity, the size of the inlet and outlet, the volume flow passing through the barn, and the heat produced by the dairy animals. Thus, measurements in the dairy barn should be made by at least several sampling points/lines in order to obtain more accurate measuring results and check the variance between sampling points.

Edouard et al. [9] analyzed the impact of positioning exterior sample sensors. If these are positioned in a way that allows exterior and interior gas concentrations to mix, incorrect emission values will be measured. This can be the case when the barn geometry and large openings on the edge cause backwards vortices (a spinning motion of the air). 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.

Janke 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. Janke 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. In this manuscript, we focus on two sampling strategies from [24]. We assume that a suitable reference method must yield ventilation rates that are highly correlated with the measured wind speed and show a low dispersion. As this reference method, we apply the direct measurement of volume flows at the inlet, based on results from Janke et al. [25], who showed on a wind tunnel model, that for perpendicular flow, accurate measurement of the volume flow is feasible with anemometers approximately every 20 m along the opening of a large naturally ventilated dairy barn. The indirect method that shows the best fit to the reference method can be used for determining volume flow in NVB. The following hypotheses were formulated: (1) Within stable cross-flow conditions, a direct method with velocity measurements about every 10 m can become a reference method. (2) Yielding this direct method as a reference method in stable cross-flow conditions identifies the most appropriate and accurate indirect method for measuring the volume flow values. Here, we focused on finding out how well the wind-related method (SM1) and non-wind-related method (SM2) estimate volume flow in comparison with the direct method.

2. Materials and Methods

2.1. Barn and Site Description

This study was based on measurements obtained from an experimental dairy barn (shown in Figure 1) in the northeast of the city of Rostock, Germany. The barn’s dimensions are 96.15 m by 34.2 m; its metal roof has a triangular shape, with the gable top reaching a maximum height of 10.7 m, decreasing to 4.2 m at the lowest point (on the sides). The total volume of the barn is 25,500 m${}^3$. The floor is solid concrete and is cleaned every 90 min by an automatic scraper. The manure then is moved by the scraper to manure pits outside the barn. The barn is naturally ventilated, with open side walls. On very cold winter nights, when the temperature drops down to the negative values, the side walls are closed using a polyethylene film. For additional ventilation under warm and low-wind conditions, four cooling fans (Powerfoil X2.0, Big Ass Fans HQ, Lexington, KY, USA) are installed on the ceiling above the feeding alley. A more detailed description of the barn can be found in previous publications [14,24,26,27].

2.2. Instrument Setup and Data Collection

In ref. [24], the authors provide a detailed explanation of the CO${}_2$ measurement procedure used in this study and the idea behind sampling lines. In this work, we use data collected from the same sample lines and with the same instrument setup. The data collection period was September 2017–February 2018.

2.2.1. Gas Data

Gas concentrations both outside and within the barn were measured using sample lines, polytetrafluoroethylene (PTFE) tubes with an inner diameter of 6 mm equipped with capillary traps every 8–10 m to ensure constant volume flow over the whole length (Figure 2). The sampling lines were positioned according to Figure 2, with two lines outside the barn (at the southern (s-out) and the northern openings (n-out), and four lines inside the barn (n-in, m-in, m-in-up, and s-in) ). The gas concentrations were measured with a FTIR spectrometer (Gasmet CX4000, Gasmet Technologies Inc., Karlsruhe, Germany) capable of switching between sample lines using a manifold. Each of the six lines was measured for ten minutes (4 min spent flushing the measuring cell and 6 min of measurement). Using this procedure, all lines could be measured sequentially each hour.

2.2.2. Wind Data

Measurements of wind direction were carried out using ultrasonic anemometers (Windmaster Pro ultrasonic anemometer, Gill Instruments Limited, Lymington, Hampshire, UK) with a 1 Hz resolution. A total of nine ultrasonic anemometers were installed on the southern opening side of the barn (inlet for southern wind directions). The southern opening was divided into 9 partial areas, and each partial area was equipped with an ultrasonic anemometer, that was positioned as close as possible towards the center of the area, based on the findings of Janke et al. [25]. On the western side above the roof of the barn (Figure 2), called the “K point”, at an approximate height of 12 m, another ultrasonic anemometer was installed to measure wind speed and wind direction.

We assumed, based on previous calculations [14,24,28] that there is a prevailing wind flow in the experimental barn that transports the exterior and interior concentrations throughout the barn and out of the outlet. Based on this assumption, we identified the prevailing volume flow (90${}^{\circ }$ south) and used only northern and/or southern sampling lines (depends on the strategy) to measure the inflow and outflow concentrations. For those cases, we also considered the wind speed values.

2.2.3. Animal Data

Obtaining the volume flow with CO${}_2$ balance method required information on the animals housed within the barn: the number of cows, their body mass in kilograms, average pregnancy length in days, and average milk yield $\mathrm{kg}{\mathrm{day}}^{-1}$. These data were obtained from administration of the State Research Center of Agriculture and Fisheries Mecklenburg-Vorpommern (LFA). The animal parameters used in this study are presented in

Table 1. Animal parameters used for CO${}_2$ balance method.

Parameter	Number of Cows [Number]	Weight [Kg]	Milk Yield [$\mathbf{Kg}{\mathbf{Day}}^{-1}$]	Days of Pregnancy [Day]
Min	353	518	34.5	89
Mean	387	667	36.7	94
Max	413	800	38.6	100

.

2.3. Total Volume Flow Calculations via the Direct Method

Calculations of total volume flow (Q) ${\mathrm{m}}^3{\mathrm{h}}^{-1}$ via the direct method were based on the fluid continuity equation, which identifies airflow based on the following formula:

$$Q_{tot}=3600·\sum _{i=1}^n·R_{velocity,i}·A{}_i.$$

(1)

where $R_{velocity}$ is the perpendicular air velocity to the face of the opening in $\mathrm{m}{\mathrm{s}}^{-1}$, n is the number of partial areas in the barn, and $A_i$ describes an partial area of the opening in the side wall in ${\mathrm{m}}^2$. Q${}_{tot}$ is the total volume flow which is flowing through the whole barn, and Q${}_i$ is the volume flow which is flowing through an area section A${}_i$ on the side wall.

The entire side opening was equipped with a net that acted as a wind shield. This net reduces the opening area, which must be taken into account with an adjusted A in Equation (1). The different permeability between sections is due to past construction. Each net grid in the old part of the building is 27 by 29 mm, and in the new part, 17 by 29 mm. Based on the sizes and number of grids, we reconstructed the full opening area and used this value as a permeability coefficient ($K_{per}$) in calculations of the parameter A (the area of the opening in side wall, ${\mathrm{m}}^2$).

Parameter A (the value ranging from 19.72 ${\mathrm{m}}^2$ until 32.91 ${\mathrm{m}}^2$) is a reconstructed opening area without the net. In Equation (1), $R_{velocity}$ was obtained from vector decomposition and adjusted according to the barn’s position. Figure 1 shows a view of the southern wall with the location of ultrasonic anemometers in each section. We obtained values of Q for each section and then summed all volume flow values over nine sections to identify the total Q for the barn.

2.4. Total Volume Flow Calculations via Indirect Method

Estimates of total volume flow were obtained using the CO${}_2$ mass balance method. The method was previously described in detail [17,21,22,24,29,30,31]. The CO${}_2$ mass balance method is based on the measurements of exterior and interior CO${}_2$ concentrations; estimates of CO${}_2$ production, which varies due to animal physiology; time of day; and animals’ physical activity [6]. All of these factors are considered in the calculations of volume flow.

$$Q_{indir}=\frac{C_{prod}}{\left(C{O}_{2in}-C{O}_{2out}\right)}.$$

(2)

where Q${}_{indir}$${\mathrm{m}}^3{\mathrm{h}}^{-1}$ is the volume flow; CO${}_{2in}$ and CO${}_{2out}$ are the concentrations of CO${}_2$$\mathrm{g}{\mathrm{m}}^{-3}$ inside and outside the barn, respectively. C${}_{prod}$ is the estimated CO${}_2$ production rate per animal in $\mathrm{g}{\mathrm{h}}^{-1}$, and is calculated following [30], taking into account the live weight, milk yield, activity, and days of pregnancy of the animals.

2.4.1. Sampling Method 1

SM1 is a wind-related method. Since we sorted out only southern wind direction cases (we assume an angle 90${}^{\circ }$ south, 135–225${}^{\circ }$ + 17${}^{\circ }$ spin to the north–south axis adjustment due to the barn location, thus the resulting angle is 152–242${}^{\circ }$), the stable cross-ventilated conditions were created. Thus, the wind flow approaching the barn on the southern side is considered as the inlet (Figure 2, s-out ). For the outlet (inside concentration), we considered the northern inside sample line (Figure 2, n-in). Details can be found in [24].

2.4.2. Sampling Method 2

Exterior gas concentrations typically have lower values than the interior since the source of the gases is inside the barn (dairy animals); thus, for the outside concentration, we considered that the sample line measures the minimum concentrations. The inside concentration is the average of all sample lines in the barn (see Figure 2, s-in, m-in-up, m-in, n-in).

2.5. Tukey Ladder of Powers

The Tukey ladder of power [32,33] is sometimes also called the bulging rule, and it is a non-linear transformation which works very well with skewed data, transforming them into normal or near to normal distribution, reducing heteroscedasticity. In 1977, John Tukey created a table with numbers of raising the data, called “table of power”. This table can have an infinity number of powers; however, in common use, values vary from −2 to 2. Alternatively to polynomial regression, Turkey suggests to use Equation (3) to transform data, where $\lambda$ produces the relationship between x and y to be as close to a straight line as possible.

$$y=b_0+b_1{x}^{\lambda }\mathrm{or}{y}^{\lambda }=b_0+b_{1}x$$

(3)

Classical simple transformation of data, such as log (broadly used in agriculture), reciprocal, squared, root, etc., do not always work well on skewed data. However, the Tukey ladder of power [32], Box–Cox power [34] or Yeo–Johnson transformations [35] can provide more accurate results. In order to improve the quality of data used in this manuscript, we checked log transformation, Tukey ladder of power, Box-0Cox power transformation and Yeo–Johnson transformation; the Tukey ladder of power approach provides the best transformation of the data near to a normal distribution. Therefore, we transformed all available data within the Tukey ladder of power approach.

2.6. Verification Analysis

We employed the values of the total volume flow obtained from both the direct (Q${}_{dir}$) and two indirect methods Q${}_{indir}$ for verification analysis. Overall, for the period of September 2017–February 2018, we collected measurements of CO${}_2$ concentration outside (two sample lines) and inside (four sample lines) the barn, wind speed, wind direction (from the K point and nine anemometers on the southern wall), inside air temperature and animal parameters required for the mass balance method. The data had hourly resolution and were used to calculate total volume flow via direct and indirect methods. In order to normalize the results, Q values were harmonized by using Tukey’s transformation. Normalization is required to assure meaningful results of the correlation analysis and statistical tests.

2.7. Correlograms (Corrgrams)

Comparison between direct and indirect methods was conducted using the correlogram (or in some sources, it also called “corrgrams” [36,37]) function available in R (version 1.0.143), package PerformanceAnalytics. These plots present correlation statistics via intercomparison analysis between several methods in the way of a chess board. Along a diagonal line, histograms for each method are presented. As additional information about methods, bivariate scatterplots are presented on the left side, and correlation coefficients on the right.

3. Results

3.1. Statistical Analysis of Volume Flow

Further, Pearson correlation coefficients were calculated between the direct and two indirect methods, as well as the wind speed (data obtained from the K point), and the resulting correlograms are presented in Figure 3. Each column and row contains results obtained for the corresponding method.

The histograms (Figure 3, diagonal line) show that after the Tukey ladder of power transformation, data became near to normal distributed, near symmetric and can be further analyzed. Thus, we can confirm that Tukey transformation converts even skewed data of different types very well.

Both SM1 and SM2 are relatively highly correlated with the direct method (Pearson correlation coefficients are 0.74 and 0.78 correspondingly; all correlation coefficients are significant with the threshold of 0.95) and have good correspondence between each other. Additionally, they have high correlation with wind speed. The last column in Figure 3, with the results of the correlation analysis between two indirect and one direct methods, show that the direct method has a strong significant correlation (0.88) with wind speed. Since the direct method has a strong correlation with wind speed, this confirms our initial assumption that the direct method is an appropriate reference method in clear cross-wind conditions. The indirect methods also show high correlation coefficients; SM2 has the correlation of 0.87, and for SM1, the correlation coefficient is 0.81.

Bivariate scatterplots (Figure 3) show acceptable agreement between the direct method and SM2 (coefficient of determination $R^2$ is 0.61), whereas SM1 has higher dispersion around the fitted line (coefficient of determination $R^2$ is 0.55). We noticed that the two indirect methods are strongly correlated (3rd column, 2nd row). The scatterplots obtained for wind speed and direct methods are also in a good agreement.

Between wind speed and indirect methods, a high dispersion for high wind speed values and several outliers was noticed. The fitted lines have a linear positive correlation with direct, indirect methods and wind speed. We can conclude that the dispersion of values for direct method and wind speed is the lowest. The dispersion for SM2 is slightly lower in comparison with SM1.

In the next step, we calculated standard deviation (sd), mean, median and root mean square error (RMSE); the outputs are presented in Table 1. The values are presented in two ways: values of Q in ${\mathrm{m}}^3{\mathrm{h}}^{-1}$ and in relative difference (in %) toward the direct method. The comparison between $s{d}_{dir}$ and $s{d}_{ind}$ for each method showed that SM1 provides the lowest standard deviation (the values are higher on 83% in comparison with direct method), whereas SM2 shows higher values (the difference between direct and SM2 is 107%). By RMSE, the results have similar distributions between methods: the lowest RMSE is again obtained for SM1 (RMSE = 642,763), the highest is for SM2 (RMSE = 974,368). The median values for all methods are lower than the mean values, which demonstrate not perfectly symmetric distribution with the distribution slightly skewed to the right.

3.2. Measured Volume Flows

The mean values obtained for two indirect methods and the direct method are displayed in Table 1. They show that SM1 has the lowest mean (however, still higher than direct method on 58%) and again, SM2 shows the highest differences with the direct method (higher on 123%).

Figure 4 shows the calculated pairwise differences of measured volume flow values with the three methods as boxplots. Comparison obtained for the pairs Direct-SM1, Direct-SM2, and SM1-SM2 is displayed. It is seen that boxplots are overlapping, That is why a Bonferroni t-test was carried out in order to identify the existence of significant differences between the mean values in the groups (Direct and SM1; Direct and SM2; SM1 and SM2). The p-values obtained using the Bonferroni t-test showed significance with the confidence interval of 95%, presented on top of the figure. Looking more specifically on each part, we can conclude that the pair “Dir-SM1” shows the lowest differences and again, Q values obtained via SM1 corresponds better with the direct method. The pair “Dir-SM2” shows higher differences and less correspondence with the direct method. The pair “SM1-SM2” shows that even between the indirect methods, the Q values are highly different.

Looking at each method separately and their statistical values presented in Table 1, we can conclude that the direct method shows the lowest spread of the values with the lowest mean value. SM1 shows higher values than the direct method by 58% and generally lower values than SM2. SM2 has a wide range of values, with a much greater spread. In this case, SM1 shows values (See Table 1) much closer to the direct method in comparison with SM2.

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, Wang 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. Janke et al. [24], Saha et al. [28], Zhang et al. [38], Schrade et al. [39] stated that in the cold period, the volume flow values are generally lower, and in the warm period they are higher. König 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. Wang 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.

In SM2, the averaged indoor (for CO${}_{2in}$) concentrations and sampling line measures of the minimum concentrations (for CO${}_{2out}$) are taken. The difference between these two values is presented as a denominator in Equation (2)). It was noticed that this differences is systematically underestimated due to the air mixing in close proximity to the inlet of the barn, and as a result, it overestimates the total volume flow [40].

However, SM1 uses the northern inside line for inside concentrations. This line may not be able to catch concentrations precisely within the main outgoing flow under more buoyancy-driven flow conditions, which appears due to the temperature differences outside and inside the barn. The latest research on the question of the correct positioning of sampling lines show [41] that the height of the measurement line is particularly important. A sampling line close to the outlet can be, in principle, used within each convection scheme. However, the optimal height of the line differs considerably among the convection regimes. As a result, the wrong height selection can bring large errors. However, the optimal height of the line differs considerably among the convection regimes between 1.5 m and 2.5 m typically (or 33% to 55% of the opening height) when the magnitude of the incoming air velocity became more dominant (mixed to forced convection schemes the optimal height tends to lower values, even below 1 m for winds higher than 3 m s${}^{-1}$). For buoyancy-driven flow, under cross-flow conditions, the optimal height is believed to be around 2 m. In terms of sd, the values for both indirect methods are higher in comparison with the direct method. This could be because even after the Tukey ladder of power transformation, the values of direct and indirect methods are still slightly skewed right (this can be concluded based on the differences between the median and mean). It was noticed, within low velocity, that the measurements become more uncertain. Distribution of sd values (see

Table 2. Statistical characteristics obtained for $Q_{dir}$ and Q ${\mathrm{m}}^3{\mathrm{h}}^{-1}$ from two indirect methods for the research period. $RD$—means relative difference in %. Parameters with the notation (exp) were transformed back to their initial units using exponential transformation.

Stat.Type	Direct	SM1	SM${}_{\mathit{RD}}$1	SM2	SM${}_{\mathit{RD}}$2
Corr	-	$0.74$	-	$0.78$	-
RMSE (exp)	-	$\mathrm{642,763}$	-	$\mathrm{974,368}$	-
sd (exp)	370,063	677,419	83%	767,976	107%
mean (exp)	644,400	1,020,816	58%	1,440,346	123%
median (exp)	587,589	837,680	42%	1,306,364	122%

) for indirect method show that SM1 obtained much lower sd than SM2. SM2 shows considerably high sd. It overestimates the total volume flow, and the mean value is also relatively high. This might happen due to the systematic bias, which in turn appears because of the relatively small differences between the inside and outside concentrations, leading to higher volume flow values. In SM2, we collect data from all sample lines inside the barn, including the middle lines. The southern and middle lines contain relatively lower concentrations than the northern sample line, resulting in lower inside concentrations for this method than for SM1.

It has to be noted that the analysis performed by the authors of [24] led to the conclusion that a wind-related sample method (such as SM1) is more accurate in stable cross-ventilated conditions, and one (such as SM2) based on average concentrations inside the barn works better in more complex wind conditions. In our work, we noticed similar outputs, where SM1 show more accurate values toward the direct method than SM2 in stable cross-ventilated conditions. Statistical values and the spread of the values obtained for SM1 are more accurate toward the direct method than for SM2, where SM2 values greatly overestimate the volume flow values in comparison with SM1.

It has to be noticed that the seasons when the data were obtained play also a crucial role on the results. The authors of [24] considered measurements for the whole year and provided a comparison of the result based on literature review. In our work, we used only autumn–winter measurements and compared the results of all methods to those of direct sampling. Different seasons and reference methods can lead to different results. This must be taken into account when selecting the sampling method for a particular measurement setup.

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.