## 3 Results and Discussion
### Comparison between Analysers  
The analysers agreed well with each other on the measured NH\({}_{3}\) concentrations (Table 2). Among the total of 30 trials, six trial-measurements from the Rosemount analyser and two from the Gasmet analyser were unavailable due to system malfunction. Because of the different observation ranges and uneven weighting of error in the root-mean-squared estimation, the obtained \(r\) and RMSE estimates of Axetris will be discussed separately. Excluding Axetris, the pair-wise correlation coefficients were \(>\)0.998. The RMSE among the analysers varied between 0.27 and 1.85 ppm\({}_{\rm v}\). The smallest difference was found between Picarro and Gasmet, and the largest difference between INNOVA and Gasmet. Picarro had the lowest error with respect to the mean of all the analysers, and INNOVA error was the highest.  
The analysers also agreed well on the temporal pattern of the NH\({}_{3}\) concentration. An example of the measured NH\({}_{3}\) with 130-second time resolution in the pig barn is given in Figure 1. During this measuring period, the barn was neither actively ventilated nor heated, and the indoor temperature followed the typical sinusoid diurnal pattern where the peak appeared around 15:00. Despite the absence of pigs, the NH\({}_{3}\) concentration fluctuated between 15-27 ppm\({}_{\rm v}\) and the details were captured by all of the analysers. Noticeable relative biases among the analysers can be clearly seen on the time series plot, but the offsets were moderately consistent during the test period. The measured NH\({}_{3}\) values from INNOVA remained the lowest and Axetris the highest.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & **INNOVA** & **Picarro** & **Rosemount** & **Axetris** & **Gasmet** & **Mean** \\ \hline \multirow{4}{*}{**INNOVA**} & & \multicolumn{5}{c}{RMSE [ppm\({}_{\rm v}\)]} \\  & & - & 1.078 & 0.646 & 1.846 & 1.216 & 0.872 \\
**Picarro** & 0.999 & - & 0.637 & 0.542 & 0.462 & 0.300 \\
**Rosemount** & \(r\) & 0.999 & 1.000 & - & 1.205 & 0.562 & 0.327 \\
**Axetris** & 0.889 & 0.971 & 0.976 & - & 0.272 & 0.750 \\
**Gasmet** & 0.998 & 0.999 & 1.000 & 0.991 & - & 0.424 \\
**Mean** & 0.999 & 0.999 & 0.999 & 0.936 & 0.999 & - \\ \hline \hline \end{tabular}
\end{table}
Table 2: Pair-wise correlation coefficients (\(r\), low-left diagonal) and root-mean-square errors (RMSE, upper-right diagonal) among five tested gas analysers and the mean on measuring ammonia (NH\({}_{3}\)) (ranged between 0.98 and 19.1 ppm\({}_{\rm v}\)) in the field over 30 trials. The mean represents the unweighted average of available analyser measurements per trial.  
While the Pearson's correlation coefficient values are very high (Table 2), the estimates are insufficient for representing agreement because systematic biases are not accounted for [22]. More comprehensive tools may be the concordance correlation coefficient [23] and Bland-Altman analysis [24]. Still, high linearity is a crucial basis for linear calibration. Because the Pearson's correlation coefficient is one of the assessment criteria in EN 14793, the \(r\) values are calculated to allow for direct comparisons to the results from the equivalence test.  
The available measurements of the Axetris were between 15-19 ppmv, which was evidently smaller than the 0.8-20.9 ppmv observation range of the other analysers. This lead to an issue that the estimated \(r\) values for Axetris tended to be smaller than the \(r\) values for the other analysers. To cope with the range difference and obtain indicative estimates, Thorndike's Case 2 [25] was applied to calculate correlation coefficients of the Axetris measurements over 0.8-20.9 ppmv. After expending the observation range, the \(r\) values were significantly improved, and the lowest correlation was found between Axetris and INNOVA (\(r=0.997\)). For the high concentration range observed in the pig barn, the RMSE between analysers other than Axetris was 0.98 \(\pm\) 0.78 ppmv. This was comparable to the 0.92 \(\pm\) 1.21 ppmv RMSE for Axetris (Table 2).