## 1 Introduction  
Climate change is one of the great challenges of our century. In order to develop adequate mitigation measures, greenhouse gas emissions in all economic sectors, including agriculture, need to be soundly quantified [1; 2; 3]. In the context of livestock husbandry, methane is a substance of particular importance [4; 5; 6; 7]. It emerges during decomposition processes in manure and during ruminants digestion and makes up about 44% of the sector's greenhouse gas emissions [8]. The Food and Agricultural Organization (FAO) of the United Nations estimated that dairy cattle husbandry contributes 20% of the total greenhouse gas emissions from the livestock sector. One important issue in this context is that the emission dynamics from the digestive system of the ruminants and from the manure are different. Emissions from manure are expected to increase exponentially when the ambient temperature is above approximately 15 \({}^{\circ}\)C, while emissions from the digestive system follow rather a parabolic curve in dependence on the temperature with minimal emissions from lactating dairy cattle at ambient temperatures around 10 \({}^{\circ}\)C [9; 10]. Particularly when housed in barns with solid floor and manure scraper (i.e., no significant manure storage inside the building), a substantial part of the methane emissions from dairy cattle husbandry is associated with the fermentation activity in the rumen, where approximately 92% of the gas leaves the body via eructation and breath [11]. Although there are mechanistic models that predict the emission of individual cattle, the evaluation of methane emissions on the housing level is challenging [12; 13; 14; 15]. Besides temperature, animal and farm-specific parameters (e.g., feed composition and feeding time) as well as local air flows affect the overall emissions. The latter is particularly challenging as dairy cattle (if not on pastures) are commonly kept in naturally ventilated buildings where indoor air flow is governed by constantly changing inflow conditions. A continuous measurement of the methane emissions from such buildings is, however, barely possible since the area of inlets and outlets is large and the openings are dynamically changing their role as inlet or outlet in response to the varying ambient conditions. This, besides technical challenges, results in high expense for monitoring the inlet and outlet openings and a preference for intermittent measurement strategies [16]. In many studies, air exchange rates and gaseous emissions are estimated by balancing gas (particularly CO\({}_{2}\)) inside and outside the building on a few days distributed over the year. It is recommended to include hot, cold, and moderate days [17]. Annual emission values are derived from those measurements by using weighted averages or regression equations based on easy accessible explanatory variables (e.g., ambient temperature, inflow wind speed, herd composition, floor type, etc.). In the past, this procedure was frequently applied to model ammonia emissions and extrapolate to annual ammonia emission factors, where in most cases a multilinear model was fitted to the logarithmized emission values [18; 19]. With more and more data being compiled the interest in testing machine learning approaches in the context of emission modeling continues to increase with first promising results [20; 21]. It has been recently observed for ammonia emissions from a naturally ventilated barn that the procedure of fitting multilinear models is rather sensitive to outliers in the measurements while the robustness of the prediction can be improved by applying advanced data science approaches (particularly ensemble methods) [21]. Uncertainties of around 20% have been found with current sampling strategies even with machine learning in that study.