## 4 Discussion
### Role of Individual Features  
Our correlation analysis indicated that particularly the day-time components can explain a substantial part of the variability in the emission of methane from the naturally ventilated barn with concrete floor considered in this study. The key role of the day-time components is likely closely related to the fact that methane emissions are essentially determined by the feed intake [4]. In consequence, the timing of feed supply and milking is a central clock for the circadian rhythm of methane emissions. In husbandry systems with feed supply in the early morning, at midday and in the afternoon three peaks were reported in literature [46]. For feeding systems with feed supply in the morning and the afternoon a bimodal distribution of methane over the day has been reported [4]. In contrast, for systems with feed supply in the early and the late morning, as on the farm in our study, there is  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Scenario** & **MAE** & **RMSE** & **R\({}^{2}\)** & **TAE** & **TAE** \\
**Unit** & **g h\({}^{-1}\) LU\({}^{-1}\)** & **g h\({}^{-1}\) LU\({}^{-1}\)** & **\%** \\ \hline
1 & 1.692 & **2.223** & **0.394**  
+++ ==WARNING: Truncated because of repetitions==
& 0.040 & 0.344 \\
2 & 1.394 & 1.898 & 0.559 & 0.053 & 0.459 \\
3 & 1.352 & 1.843 & 0.584 & 0.227 & 1.961 \\ \hline  
++  
typically one pronounced maximum of methane emission over the day [10; 47]. These diurnal rhythms that are discussed in the literature do not only explain the high absolute value of the correlation coefficient between the day-time components and the methane emission, but also why the correlation in our case is negative. With feed supply on the farm in our study in the early and late morning the emission maximum is observed in the late afternoon [10]. This timing of the maximum coincides neither with the maximum of the sine nor the maximum of the cosine, but is phase shifted relative to the trigonometric functions. In consequence, negative correlation coefficients were obtained. The observed diurnal rhythms in methane emissions can, however, not only be explained by feed supply as even on pasture, where feed is continuously available, diurnal patterns of the methane emission have been found [48]. Other possibly influencing variables besides feed supply are the change between light and darkness and the ambient temperature, both affecting the general activity level of the animals. Preceeding studies have indicated, that methane emissions notably depend on the ambient temperature. Considering large temperature intervals, an increase of the methane emission towards both edges of the thermoneutral zone (i.e., the temperature interval where most of the metabolizable energy can be used for production) was reported in literature [10]. This immediately suggests that a consideration of the ambient temperature as a linear variable alone is not enough, which is also indicated by the low correlation coefficient in our analysis. In consequence, the consideration of the squared temperature as a feature is valuable for the modeling of the emissions, which is indicated by the correlation coefficient that is almost twice as high for squared temperature compared to the temperature itself. It has also been found that, after an increase of the methane emissions under mild to moderate heat stress conditions, under severe heat stress methane emissions go down again [49]. However, under the typical climatological conditions in our study region squared temperature can be expected to be sufficient to model the influence of ambient temperature on the methane emission. High wind speed can reduce heat load and thus modulate the emission pattern induced by the ambient temperature [50]. Moreover, high wind speed is associated with a larger volume flow from the naturally ventilated building and can thus result in higher emissions in general as less of the produced gas is trapped inside the building. Our correlation analysis, however, indicated that these effects play a minor role.