## 2 Materials and Methods
### Calculating Fluxes Using the Gradient Flux Method
#### Calculation Approaches for Soil Gas Fluxes  
Even though the mathematical-physical description included in the gradient-flux method is valid and accurate, there are uncertainties that come with the practical implementation that need to be considered. They result from uncertainties in laboratory measurements of soil physical properties (total pore volume, diffusivity), in situ measurements and modelling (soil water content, soil gas concentration). In addition, spatial heterogeneity and discrete sampling (in time and space) allows only for grasping a snapshot of the reality. There are different practical approaches to calculate soil gas fluxes from discrete soil gas profiles [44] that were developed to address different challenges [50; 64; 102; 60]. The calculation approach can substantially affect the calculated efflux and the partitioning within the profile [76] and should be carefully chosen. To test and demonstrate the effect of the calculation approach on gas flux estimations we included four different approaches. Soil gas fluxes were calculated at defined depths by multiplying the gas concentrations gradients with D\({}_{\text{S}}\) of the respective soil layer (Equation (1)). Soil and humus were split into three layers with constant total pore volumes: humus layer, 0 to 5 cm depth, and 5 to 10 cm depth. Total pore volume and soil water content were input data to our site and depth specific diffusivity models to calculate profiles of D\({}_{\text{S}}\)/D\({}_{0}\). Including \(D_{0}\) allowed deriving the \(D_{\text{S}}\) of each gas (Equations (4) and (5)). \(D_{0}\) was adjusted to the current temperature and barometric pressure [93], which was derived from a weather station nearby of the German Meteorological Service (DWD) and corrected for differences in altitude when own pressure measurements were lacking. The harmonic mean of the \(D_{\text{S}}\) profile between the respective gas sampling depths was calculated as representative average of the respective soil layer [103]. In contrast to many other studies, we had five soil gas samplers per depth at four to five different depths in the soil to obtain a representative gas profile in the humus layer and the top 10 cm of the mineral soil. If only one concentration measurement per depth is available, as in other studies, the calculation of the concentration gradients in the soil is a simple approach of discrete differences [50; 64]. With several measurements per depth different regression approaches can be used [44; 76]. The same \(D_{\text{S}}\)/\(D_{0}\) data were used for all flux calculation approaches. The first approach is based on local linear regressions (LL) that is done for all soil layers separately [76], i.e., all concentration measurements from 10 to 5 cm depth were used to calculate a representative concentration gradient for the respective layer using a simple linear regression function. The same was done for the \(-5\) to 0 cm layer, and then the humus layer. The second approach is a linear regression (LR) across the entire soil gas profile for which all concentration measurement from the atmosphere to 10 cm depth were used to calculate one average concentration gradient for the entire profile [64]. As third approach, we used a linear spline function (LS) with a node at the soil-humus interface (0 cm depth) and at 5 cm depth in the mineral soil. The derived fluxes of the LL and LS approach were assigned to the middle of the respective layers. The fourth approach fits an exponential function (EF) for the entire concentration profile [60]. The soil-atmosphere flux of CO\({}_{2}\) and CH\({}_{4}\) was calculated using all four approaches to compare the different calculation approaches. Since the LL and LS calculation approaches are not able to estimate the concentration gradient at the soil-atmosphere interface directly, the flux estimations in the humus layer and in the 10 to 5 cm depth layer were used to extrapolate the flux to the surface [104].